No. Disarming Attack isn't useless.
Here's my reasoning:
To determine if the Disarm option makes the Disarming Attack battlemaster maneuver useless, we need to compare a situation where either one or the other could be used — that is, whether a fighter who can make a Disarming Attack is always better off attempting a Disarm instead.
I took some stats for a typical 3rd-level Battlemaster fighter: AC 18, 34 HP, +6 attack for d8+6 damage, DC14 for saves vs. their maneuvers. I then looked at a few CR 1/2 - 2 creatures and the expected results when the fighter attempted a Disarm against the creature vs. the results when she used Disarming Attack.
Note that a creature that doesn't have Athletics or Acrobatics proficiency doesn't automatically lose the Disarm contest; they just use their Strength or Dexterity modifier instead. So it's not really accurate to say (as expressed in the question) that those creatures don't have the skills to defend themselves. Likewise, all creatures have a Strength saving throw, and have a chance to save against Disarming Attack.
Generally speaking:
Disarm has a much higher chance of success (in the 50-70% range ), since it doesn't require a successful hit first.
Disarming Attack has a much lower chance of actually disarming the creature (in the 25-35% range), since it requires the attacking fighter to first overcome the creature's AC, and then for the creature to fail its saving throw.
The other tradeoffs between the two are enumerated in the question itself; the most significant of these is that Disarm does no damage, and Disarming Attack always does above-average damage (due to the superiority die) on a hit, even if the target isn't disarmed. This means that the basic comparison between the two options is that Disarm has a high chance of disarming but never does damage while Disarming Attack has a lower chance of disarming but does above-average damage.
So the key question is: under what circumstances is it more useful to disarm an opponent than just do damage to them? Bear in mind that causing a creature to drop one of the weapons it's holding doesn't mean it's no longer a threat. Many creatures carry multiple weapons, or have natural attacks such as biting that can't be disabled with a disarm. Creatures can also slam or grapple, or try and recover their weapon, or even attempt to disarm their attacker.
One scenario where Disarm might be useful is against hard-hitting creatures with moderate hit points. A bugbear is a typical example; their attack does a lot of damage, but their hit points aren't so low that it's safer to just try and kill them quickly. A successful Disarm attempt will reduce the threat they pose and buy the fighter some extra time to chip away at their hit points (assuming it takes the bugbear on average more than one turn to recover from being disarmed). This isn't the case against a creature like an orc, with fewer hit points; our fighter is probably better off using Disarming Attack (which, if it hits, has a good chance of killing the orc outright) or just making regular attacks. And against a higher-CR creature with more hit points, like a Bandit Chieftain, the couple of rounds that a Disarm might buy the fighter isn't enough to offset the creature's higher hit point total significantly.
Combat situations can vary greatly, of course, at at higher character levels and monster CRs it becomes much harder to model. I think it is safe to say, however, that because it doesn't deal any damage, Disarm isn't always going to be a better choice than Disarming Attack for a character who can use either one.