This is going to become grittier
To sum up: changing this will lead to a roughly 10% higher mortality rate in tier one play. It will become less at higher levels, but still increase.
As you can see from the table you included in the question, this type of critical implementation will lead to higher damage output -- it's nearly the same for exploding d20 (as double exploding there is very unlikely), but compared to the 1 in 20 critical hit chance on a nat 20, the percentage of added damage is higher for all the dice, the higher the smaller the dice. On a dagger dealing d4, you will get 33% more damage instead of the 5% you get from the d20 crit system.
How high is the chance for a KO punch?
However, what is more important to your question, this system does have a chance to reach some rather high single hit damage levels -- as you say, theoretically unlimited high, but in exchange also being unlimited unlikely. In practical terms you can use these functions on anydice to see how likely it is to get an extreme outcome on a single hit, setting the output table to "at least":
output [explode d6] named "explode d6"
output [explode d8] named "explode d8"
output [explode d10] named "explode d10"
output [explode d12] named "explode d12"
And below is the output for a d8, for example
As you can see, the probability for exploding 3 times, for at least 25 points of damage, is about 0.2% here, and the higher values are not shown.
Much like with normal criticals, this is especially deadly at lower levels, as you do not need a lot of consecutive explosions to take the characters out. Even with some light Constitution bonus, typical characters maybe have around 10 hp on the first level, 16-17 on the second level, 24-25 on the third level, and 32-33 on the fourth level.
That means a d8 hit would have a 0.2% chance to outright drop a character of level 1-3. If you move up to a d12, you have a 0.23% chance to deal 33 or more, dropping a character up to level 4.
How many punches will you take?
The issue is that over the course of their career, the characters get hit many, many times. Just roughing it out, with an average combat maybe taking 3-5 rounds, attacks hitting about half the time, and the typcial day having maybe 3 combat encounters, you get a ballpark of 6 attack hits per character and day -- lets triple that, because there may be multiple weaker opponents that have more attacks in total, and stronger opponents often have multi-attack routines, and round up for good measure. We do not need to be super exact to get an idea. This could mean about 20 attacks per day of adventuring.
According to the rules in 5e, it would take you about 33 days to go from level 1 to 20, if you remove rest days and such. To get to about level 12, where many campaigns tend to wind down will take you about 24 days. You spend about 6 days of combat in tier one, good for about 120 times being hit.
You have a 20% chance to get hit by a triple-exploding d8 during that time, an 11% chance to get hit by a quadruple-exploding d6 that likewise deals more than 24 damage, and looking at orcs, who hit with greataxes, a 24% chance to get hit for at least 33 damage, and killing you all the way up to level 4.