Back in Demon's Souls and Dark Souls days I don't care about co-op/pvp at all, I didn't even give it a try.
Back then I usually just watch YouTube videos made by those well known pvp players in the Souls community. (You know, those guys. Peeve, Oroboro, OnlyAfro etc.)
Same goes to Dark Souls 2 but I dropped it soon after getting the platinum anyway. I hated that game.
Bloodborne is probably the first Souls game that I gave coop and pvp a try, and I fucking loved it.
Not trying to brag but I never thought I could be this good at Souls pvp, part of the reason why I didn't gave pvp a try is because I am afraid that I won't even last half a minute in a fight.
In Bloodborne, I'm dropping people left and right, even when going against gankers.
The Chikage, Saw Spear and the Beasthunter Saif made me UNSTOPPABLE.
I once killed about 47 players in a row without dying once, it was a good hunting day.
Dark Souls 3 pvp was also very fun to play, but not quite as exciting as Bloodborne imo. I know the pvp is technically much better than BB, but I just don't like the feel of it.
[TL;DR]
Overall I would say that it is quite important to me, but not nearly as important as the main game.
If dropping the online aspect can somehow make the singleplayer game a better experience, then I'd say do it.
Edit: I forgot to mention that coop is probably the most boring part for me, it just kind of....break the game. It's only ever fun when I am helping people out in the defiled/cursed chalice dungeons.