Loving the optimism
I'll be honest as to why this won't work out.
As a whole CG works out "Pretty" well, but individually there's a lot of fighting between people.
There are people who I know don't like me, and for a reasonable part, I don't like them. This can be said for roughly 80% of the community and we usually stick to our respective games and avoid conflict with one another.
However, when you volunteer for something like "Game Night" you're making a commitment to play which ever game comes up, with whoever else signed up. This means there's a large chance you could be signing up to play a game with someone who either doesn't like you, or you don't like.
This will lead to fights in most games, especially ones that require Co-op. It's also become more aggressive if you happen to be playing a "Versus" game against someone you don't like.
It is a nice concept, but in the grand scheme of things it'll eventually devolve into fighting.