I've never really understood that the "varying class limits is counterintuitive" thing.
You could actually get fairly reasonable class limits close to what we have already by using 2 for attack classes and 1 for defense and support classes. (this might be even more reasonable with pyro being rebalanced). This is a solution that is consistent with existing in-game logic. Medic limit 1 is always a good place to start because medic is the most powerful class in the game and the only actual support class so teams are going to run as many as they can (within reason) of them.
A bigger problem with the current format is probably that it's way easier to defend than to attack and some of this comes from the fact that there's a complete lack of diversity for current class roles in the game.
To break a stalemate you have to create an advantage somehow- scout and soldier can do this through getting picks/creating space/doing damage/forcing. Demoman can do this to a lesser extent as he does fill more of a defense role. Sniper and spy are an alternative that can be used as a pick class but both are easily counterable by smart teams and still don't necessarily allow the team to push off the 1 pick, as well as a sniper often making the other team play even more conservatively. Pyro is quite clearly not an attack class despite being grouped as one and heavy and engineer are absolutely the worst classes for breaking stalemates as they're based on area denial.
If valve are looking towards creating their own format/ruleset they should look to try and create a healthy balance between stalemates and breaking them. Having periods of downtime and then pushes is no bad thing- if the game was constant teamfights then it would also be unenjoyable to watch and very difficult to cast.
Right now though, it's pretty clear that once a stalemate is established it's really hard to break out of it against a good team in the current meta. I think the pacing of the game is probably one of the things most key to its success and when players complain about the game being "aids" it's normally either because it's way too stalematey or because there's always something going on. Some gamemodes like highlander and payload especially suffer from this because of the increased player count and because the objective is constantly being played as opposed to in short bursts like with control points.