Overwatch isn't really taking TF2's crowd though. On the surface they're similar, but mechanically they are worlds apart. Overwatch is highly polished; TF2 is downright clunky by comparison. But it allows custom servers and player scripting/mods. Blizzard is far too tight-fisted for that to realistically happen for Overwatch. TF2 also has all kinds of interesting movement mechanics due to the source engine, that overwatch just really doesn't have. Overwatch's format of merely 6-person teams means you can't really goof around like you can with TF2's 12 and 16-person teams.

I'm sure a lot of players checked out overwatch but didn't stop playing TF2 as they're simply very different games. TF2 also did release major updates albeit infrequently until the jungle inferno update back in ~2017. Now it's just radio silence apart from small seasonal updates.

I'm not as familiar with CS (only played a few dozen cs:go matches), but just from playing both that and valorant I feel like it's going to be a similar situation. Valorant is more polished but it just plays wildly different due to the player abilities.

Valve is neglectful regarding these games (look at how DotA 2 is treated by comparison), but I doubt trying to compete would've helped very much.