I think they care but they don't know how to care in a way that makes the game better and people are happy with
Someone mentioned it on this forum recently (I'd quote it if I could find it), but with the recent CSGO changes to make tapping better people were asking for that for months if not years, and they only just implemented it. They only nerf weapons if stats say that they're overused, instead of looking at community consensus on weapons (the exact reason none of the tf2 weapons we ban will ever get nerfed or changed). Anyone could have told them that the reserve shooter is stupidly broken, but according to b4nny in that one stream clip apparently they were going to buff it.
As opposed to Blizzard and Overwatch, where the devs working on the game actually realize "oh shit, no one wants to play against stacks of a single hero in competitive" and put a 1 hero limit on comp. If it was Valve, they would have waited until stats show that 90% of games are comprised of games of multiples of one or more hero, and probably wouldn't have even considered putting a limit unless literally every game was a 6 stack of the same hero.
I'm willing to believe Valve (or the 3 people working on the game) care about it, but they're not the best at realizing that what the community at large wants is actually the best thing for the game. I'm also still a bit mad that they haven't explained why they think viewmodels need to be forced on, and I don't buy "evening the playing field for all" as a good enough reason. The cynic in me just says they're forced on so that skins are more visible in streams and stuff and they can make more money off the game, but they'd never admit that.