I can't say for 960 specifically, but for standard chess getting rid of castling usually results in the players just manually castling their kings. I believe that is why the move was introduced in the first place. So it really doesn't accomplish much except make the opening a bit more limited, since they have to leave themselves a way to manually run the king over one of the rooks. Usually to the short side, since that's quicker. Basically makes queen side much less viable to leave the king at. And queen side castling was already the rarer of the two options. I imagine it would be a similar story for a lot of 960 positions. I'm not sure how getting rid of castling would benefit anything. In 960 you already get a lot of super crazy aggressive positions with exposed kings even with castling.