Gaming may be "worth more" but culturally it's still frowned upon. With smartphones, you can "hide" the fact that you're playing. Not so easy to do that with a Switch in public.
Somewhere in the mid 00s, society established a new gamer stereotype as some lazy man child who prefers to sit around reading comics and playing games to going out and "grabbing life by the horns" or some other nonsense.
Because gaming is pretty ubiquitous and accepted in American culture (at least in the coastal areas I've been to).
Playing games and identifying as a 'gamer' are definitely different, however. I play a lot of core games (PUBG, Overwatch, etc.) but I definitely do not label myself a 'gamer'.
I had no answer for that.
Marketing video games to enhance a social setting rather than a way to escape one probably appeals to parents who are worried about the whole "screen zombies" thing.