Avoidant people want friends though. It's their biggest source of heartbreak, that they want friends but can't have them because they're sure they will disappoint everyone and will be rejected once someone gets to know them.

I think that avoidants do care that they have no social lives. I think it weighs on them constantly. Eventually they might accept that it is their lot in life, that they are incapable of having the type of relationships they want, and so they stop trying. That might be the lesser of two evils, to not have the open wound of constant rejections. But the desire is still there, even if it's been put in lock down.