The difference in the Buck/Abby relationship and the Buck/Eddie relationship is that Buck wanted to make things better for Abby and fix it, whereas with Eddie, he's stepped right into the life/mess Eddie lives and is a pillar of support. He's never tried to fix Eddie and Chris.

to the point where he's lost his sense of self, and now the Hot Priest has tasked him with discovering what brings him joy, and now he's looking at houses in El Paso and you're telling me if he moves there he's not going to lose his sense of self entirely?

Abby even says she lost her sense of self when she's talking to Buck at the end of the episode and that she was afraid if she came back to LA that she would lose herself again, and isn't that what Eddie is experiencing? He's put everyone else's needs above his own,

Or Buck goes and drags them back after like a week of him being there