Like, the crux of House and Wilson’s relationship for Wilson is that Wilson is somewhat preforming kindness and empathy, and around House he doesn’t have to. He can be fucked up and a little weird, and play increasingly destructive pranks. He can fight with house, and punch him in the face and ask him to dinner a second later and he doesn’t have to preform normality because there is genuinely nothing he can do to ruin this friendship.
And the crux of House and Wilson’s relationship for House is that Wilson see past House’s bs and sees the sliver kindness in House’s heart, the one house keeps hidden away deep under layers of sarcasm and insults. It’s not all the time, as house still gets defensive when Wilson says something that hits a “sore spot”, but House is still kinder with Wilson than he is with anyone else, he shares his fears with Wilson, and makes sacrifices to make him happy. He doesn’t have to preform his “asshole persona” because Wilson’s the only safe person to be venerable with.
This is why they need each other, because they have to preform with everyone else, and they always end up back together because we all need someone we can be authentic with, and it’s why they’re so lonely without each other.