This is NOT in your favor
What you are experiencing is called "risk aversion" -- you intuitively sense the losses of this trade more than the gains. And you are right to feel this way.
However, before we get into if this is good or bad for you, I'll make some assertions. The save DC doesn't matter, and the target's save modifier doesn't matter; at least, not individually. What matters is the target on the die.
So, for example, with a DC 14 Wisdom save against a +2 Wis save modifier, they have to roll a 12 to save. This is the same as a DC 15 Wisdom save versus a +3 save mod, or a DC 11 Wisdom save versus a -1 save mod. That is, it's the probability that matters.
The reason that we want to look at it this way is because it reduces the saving throw into a weighted coin toss. From an entire array of save DC's and save mods, the end result is equivalent to what happens if we flip a loaded coin. In the above example, if you were betting on heads they lose, we're flipping a 45 (tails)/55 (heads) coin.
This approach has an advantage. Because we're thinking of saving throws as coin tosses now, we can apply analogies to test our perspective that wouldn't be easy to apply to a die roll.
Analogies of Dice and Coins
This 7 minute video features a man going on the streets and offering people $10 of his money against $10 of random strangers' money on a coin toss, and seeing how they react. From the video, he seems to always be rejected. The reason seems to be because the participants don't want to lose their $10. They simply didn't see the gains of an extra $10 as enough to offset their risk aversion.
The man then ups the ante. He offers $12 to some, to others $15, and to others $20. Many still reject him, though this statistically puts the bet in their favor. The perceived losses still outweigh the perceived gains.
And then he offers a solution: repeat the bet of his $12 to their $10 on a coin toss 10 times. Now, some of the participants begin changing their minds, though they aren't able to explain why.
I recommend watching the video beginning at 3:03 to 4:45, where he explains why repeating the coin toss when it is weighted favorably to one side is much more favorable than when the toss is done only once.
Here's the gist: when you do only one toss, the bet could go either way. Even when it's in your favor, it's still only a single coin toss and you could still lose. But when the toss is repeated multiple times and the bet is weighted in your favor, you are almost guaranteed to win. In the example in the video, putting up a $20-to-$10 bet on a fair coin toss, there is only a 1-in-2300 chance of losing money in that scenario for the side whom the bet favors, whereas there is still a 1-in-2 chance of losing money for the same bet if it was done only once.
So: when the coin is flipped multiple times, it is in your favor if the bet favors you.
Let's go back to D&D
Now, whenever you cast a spell in D&D, the bet favors you. What you are putting up is your spell slot (your hypothetical $10 you stand to lose), and what they are putting up is the targets experiencing the spell's effects (their hypothetical $20 you stand to gain). And when the DM rolls the saving throw, it is akin to flipping a weighted coin that favors you (as if flipping a coin with a >50% chance to go your way).
So: when you cast a spell, you're making a bet that favors you. And then the DM "flips a coin".
Let us define what it means to win or lose this bet.
When you lose this bet, you completely wasted your spell slot and got nothing in return for it. Alternatively, your targets all took half damage because they all passed -- surely all targets passing the save is a failure to you as a caster.
When you win this bet, you do not waste your spell slot because some of the targets will fail their save.
So: you are going into this bet knowing that some of the targets will pass, and that's fine with you as long as most of the targets fail.
If the DM flips this coin only once, then you stand to lose the bet with somewhere between a 1-in-2 through 1-in-5 chance depending on the exact probabilities.
However, if the DM flips this coin multiple times, once for each target, then you are almost guaranteed to win. If there were three targets, for instance, and they had a +3 save mod versus your DC 18, the odds of you losing are 1-in-37, as opposed to an odds of 1-in-3 to lose the bet if the DM only rolled once.
Why this is bad for you
The DM has now increased the odds of you wasting your resources. The RAW gives you a virtual guarantee that you will not lose your spell slot when you use it to cast an AoE spell. Your DM has overruled that and made it so you often can lose it.
In the example of a DC 18 versus their +3 save mod, and the AoE targeting three creatures: your DM has made you 12 times more likely to lose as the odds went from 1-in-37 to 1-in-3. And of course, this will make anyone feel cheated.
Failure Case: Reframed
Instead of thinking in terms of "success" and "failure", ask yourself instead: how has the DM made a miniscule chance more probable? That is, when rolling multiple die, there is only a small chance all targets pass the save. How has moving to a single die roll affected the odds, and made it more likely for all of them to actually pass?
Quantifying Changes in the odds
Consider this scenario: your save DC is 19, the five targets have a -1 save modifier. You cast the spell, and so they need to roll a 20 to make it. The DM rolls a natural 20. They all pass.
Does that make you feel like the spell slot is wasted? If so, then the above table is useful for you.
The above table shows the change in odds depending on the target on die and the number of creatures affected. Previously, the odds were miniscule that all targets passed that save, but this change has amplified that chance. In fact, the odds are 160,000 times more likely now that all 5 targets pass their save if they need to roll a 20.
In my previous example of a DC 18 save versus a +3 save mod against 3 targets, the target on die is 15 and there are 3 targets. That is the 6th row, 2nd column, which shows that the odds are 11.11 times more likely for all targets to pass their save now under the single die roll regime (I rounded off to 12 above).
You might note the other side of the picture: but now they are also much more likely to all fail their save. If you are willing to take that risk, then you will not feel cheated when the DM changes the multiple die rolls to a single die roll. It is up to you to decide how much risk you are comfortable with, and how OK you are with accepting that the result of your spells will be very swingy/extreme.
Regardless of the method of rolling for saves, whether a single die or multiple die, casting an AoE spell is still in your favor. A premise of this answer is that spellcasting is akin to betting your $10 against their $20 and flipping a loaded coin that favors you. So no matter what, in the long run, your AoE spells will still do more good than bad.
However, the difference between tossing a coin once, and tossing a coin 10 times, is not negligible. It affects your odds of winning and losing every time you flip the coin. If you are comfortable with the higher swing, then there is no cause for concern.
However, as far as this question is concerned, we want to provide evidence to overturn the ruling and move it back to rolling multiple die for saves. This implies a low appetite for risk. And a low appetite for risk is concerned about the odds of loss.
I hope you are able to use this answer and convince your DM to see your way.
Response to Objections
This does not show the entire argument as it only calculates loss. What about the gains? What about the increased chance they all fail the save together?
I am not arguing from a long term perspective. Over the long run, the method their DM chooses does not matter as the same number of creatures will fail their saves whether we went with multiple rolls or a single roll to determine the creatures' saves. In other words, the long term perspective is immaterial. What I'm showing is, how does this change things for the player now? And the answer is, it changes the odds now, and they stand to lose more often as a result.
Isn't this answer mathematically incorrect?
Feel free to verify the math and show how it is wrong, so I can update this answer. As for my part:
Given a save chance of, for example, 30% (aforementioned DC 18 vs +3 save mod), to get the odds of failure for multiple die rolls: 1-to-1/(0.3^n), where n is the number of creatures. In this example, it was n=3, so the odds were 1-to-37.
The odds of failure on the single die roll case: 1-to-1/(0.3), or 1-to-3
Compare the two odds. 1-to-37 is 12 times less likely to fail as 1-to-3
Why doesn't this answer acknowledge that there are benefits to be gained from this ruling?
Pulling arguments from the other comments who have contributed to this discussion, a swingy game means more character death. The DM loses nothing when they roll once, but the player loses a spell slot when the targets save. The DM has many NPCs who can suffer the negative consequences of all targets failing their save, but the player's character can die. In other systems, swingy dice results means the players go into such games expecting their characters to die. D&D is not such a game (at least, not 5e).
Discussing risk aversion and why we avoid risk is a thing people do in real life. It's a thing that can be done in D&D too, apparently.
The benefits to be gained by the player (ie: that they can have all creatures fail their save at the same time) is not valuable in the context of the question raised, otherwise this question would not get asked in the first place. We feel loss more strongly than we feel gains, and ten good moments in the session may feel clouded by that one bad thing that happened. The fact is: if you burn a spell slot and all creatures passed that save, that sucks for you as an AoE caster.
This definition of success/failure is wrong
There are many ways we can define failure. You can say that it is not necessarily a success if only 1 creature fails the save. But that is void of context. How many creatures were there, two? Three? Four? At which point do we draw the line between success and failure for when the case is not binary? This is not a math question, but a player one, and the answer depends on you and your risk appetite. The math will change depending on your definition, but your definition is personal to you, and this answer is predicated on a low appetite for risk (as is made apparent by the way I formulated my definitions).
We can discuss what should be the right way to categorize success/failure when talking about rolling multiple saves on many creatures, but what's the point? How can the player approach his DM with this information and overturn the ruling?
If you are personally good with casting a spell and having all targets pass the save, then that is good on you. But this answer does not include your perspective, because if we adopt your perspective, then there is no problem. It is concerned about the people who aren't alright with that, because that is where the problem exists.
And that is why I use the failure definition of failure occurring when all targets pass the save: because it is not a contestable case (ie, you can't call that a win). And the players who care about getting a sort of guarantee that they will get some utility out of their AoE spells, those will be the people who have a low appetite for risk, too.