There is no correlation between beating a game on hard and doing well in multiplayer.
For example, I'm not that great in Goldeneye or Perfect Dark when it comes to missions on harder difficulty settings but I destroy other humans like my brother who beat every mission in every difficulty level as well as all Goldeneye cheats legit - on two separate occasions no less) I also did far better than anyone else in combat simulator missions in Perfect Dark.
Single player is very structured and can be derailed by the stupidest things. Multiplayer is much more wide open which allows me to fare far better. Stuff I do in multiplayer doesn't work at all in single player. Of course I'm still average when it comes to pc multiplayer.
Also why should I suffer in hard mode anyway. I'd rather enjoy it than let it collect dust.

Same here, eg the rare FPS I'll try is auto easy, whereas strategy games are normal or hard as those are my genres.
As said above, I was a lot more competitive about it in the 90s, but now I'm much more an older game tourist, have loads of games I've never even had time to install.
The OP's premise is correct though, if you want to improve, play above your comfort level.