I think the most hurtful thing about tf2 is that it made valve so much money and was really the first of their games to do that with the micro transaction system but compared to csgo and dota2 the developers never cared much for the competitive scene whereas in all the other games it was used to fund tournaments and whatnot. The graphics setting being restricted is also quite annoying in the official competitive and makes me not even want to try it even though it is something I had wanted for forever, I personally thought csgo's in game mm was pretty fun and having something similar in tf2 would've been great but at this point it just doesn't interest me anymore, csgo has a bunch of it's own problems too though and I don't play it anymore either because of them.
TF2 was honestly a really fun game competitively when I played it but years of getting neglected by the developers in lieu of their other titles and then getting too little too late wasn't too great.
Optimization is also horrible in my experience I couldn't run TF2 the last few times I tried with a stable fps so I've just given up even trying to open it at this point and I could run much better looking games with much better fps.
As for unlocks it could be a bit annoying that some unlocks were pretty much always better than stocks in 99% of situations hence you would always wish to use them or else be at a disadvantage, although many weapon ban lists partly solved this, many of them kept vital ones which were part of the meta. I never played tf2 when it had only stock and I wish I did, I tried a bit of tfc and enjoyed it with it's list of weapons. But considering that most of these unlocks could also be gotten quite cheaply from gameplay I'd say this is less major.
For classes I personally enjoyed playing all the classes and did medic for a while but maybe the fact that it was always very hard to get a medic in a pug speaks of his role and maybe it deserves to take a look at him from a fundamental level? Yes you can medic but most would agree I think that playing scout, soldier, sniper, (won't speak for demoman because I always thought he had a very high learning curve in competitive and I was always trash at him) tended to be a better experience in pugs where most players were primarily concerned with practicing their own play rather than full on strategy where medics tended to be more important.
Honestly though I think the 6v6 format was pretty good and most fault lay in valve not being interested in listening to the competitive scene and giving little support especially compared to how much money they passively made off tf2. And then seeing the support given to csgo and dota2