the influence of the ideas of Improv Acting on the play culture started dulling the notion that the actual rules and procedures of games are things worth caring about.
Can you unpack that at all? I was nodding along to most of your post, but this point puzzled me. I thought "System Matters" was one of the old Forge concepts that did manage to survive?
I think it started from a strong place, but in my view System Matters hasn't survived completely. The way I see it, the Story-Games incarnation of System Doesn't Matter is "techinques". Basically people see something, say "Oh, that's a technique that good players/GMs use", and then think it's something they can bring to every game. So take Improv Acting -- the "rules of Improv" are themselves a System in the Forge sense, but if someone thinks that the "rules of Improv" are just a thing that good players do then they'll start bolting those mechanisms onto whatever system they're nominally using. So, for example, they might be keeping their character in a much more pawn-type stance than the game expected so that they'll be able to "roll with" whatever the other players throw at them. At least I think that's what happens, with at least some people.
Interesting. I haven't noticed that as a problem, but it's something I'll keep an eye out for.
I do think there are some behaviors and skills that generalize well across many if not all tabletop games, but they're social-skills things that are worth cultivating even beyond the game context. E.g. reading body language to notice when someone is upset, bored, or slighted.