Your stove analogy is on point, I suppose that if going out to eat was the ONLY thing that gets me out of the house socially, that I'd turn away from getting a stove if I didn't have one. Trust me, if most houses came with a pool table like they do stoves, I don't think I'd go out of my way to make a big fuss about it.
My point being that I'm socially awkward, to some people's perspective. I do not get out much, and pool is one of the only outlets I have.
So in your case you are using having to go out to play pool in a similar way people that set the clock back 10 minutes use it for. Instead of having to be late by just getting ready earlier they are faking themselves to be 10 minutes early so whey they are late they are on time, you not having a table is to force yourself to leave the house and hang out with people, it is a good idea if it works for you. I go out exactly because I like to socialize or just hang out and shoot in a place with other people, watch the goings-one at the bar tables with drunk bangers, maybe run into someone I have not seen for a while. l don't play pool just to play pool, if the whole of the game was pocketing balls in your house alone I doubt I would play much.