So in The Incredibles the Supers are coerced into giving up their caped crusades and assimilate wholly into their secret Identities. However, in the opening segment we see at least one super villain, Bomb-Voyage, and Frozone talks about Baron VonRufus, his own archenemy. So we know they are a thing in this universe, as is to be expected.
Where did they go? Wouldn't the super villains be thrilled to see the Supers vanish? It's not like they had any reason to start obeying the law or care if they get sued. If Super Villains were left unchecked public opinion would again sway towards Supers coming out of hiding to combat them on their level.
However, we get the impression that the reason why public opinion turned against the supers was because they did more harm than good. I think their point is expressed in the encounter with Bomb Voyage. If Mr Incredible hadn't gotten involved with Bomb Voyage's heist, he wouldn't have resorted to using the bomb that destroyed the train tracks to escape. So, in his own way, Mr. Incredible was responsible for the injuries sustained by the passengers of the train that crashed.
Back to the Villains, as i said, even if the supers do more harm than good when they fight them, to leave them unchecked wouldn't do either, and a population of unchecked super villains would in time come to turn public opinion back towards the supers who can combat them.
This leads me to one of two conclusions: that the Government either found a way to persuade the great majority of them to assimilate as well, or else the super villain archetype became irrelevant with the end of the Super Hero era. I am inclined to think the latter. Let me explain.
If the history of society teaches us anything its that crime can't be contained. Crime breaks free, it expands to new territories. It crashes through barriers painfully and maybe perhaps dangerously. What I'm saying is crime, uh, finds a way.
What I'm saying is that Supervillains evolved in response to super heroes. As Supers brought crime to its knees, supervillains emerged to combat them, criminals that could fight supers on their level. Without supers, super villains would no longer need to exist.
This idea fits in with the theme that "if everyone is super, no one will be". Let me use Syndrome as an example. Why did he do what he did? Because of a deep seated hatred of supers. Why was he able to succeed? Because supers wouldn't set aside their super hero personas. He lured them to Nomanisan Island under the guise of having them moonlight hero work, when in reality he was using them as beta subjects to test his ultimate weapon to defeat the most powerful super of them all. Had the heroes recognized that their time was over and refused Syndrome's offer, Syndrome never would have succeeded. The existence of Super Heroes gave rise to a super villain.
A minor kink in my theory is the Underminer scene at the end. It could be the dawn of a new age of supers, a new age of super villains is emerging, so a new age of supers must rise again to counter it.