It sounds somewhat interesting, although I feel most of the time you'd want to castle with your rooks anyway.
One of the main purposes of castling is letting you connect your rooks, and you can't do that while castling with other pieces.
Possibly the biggest difference this might make is you can still castle with a rook after moving it...
When the Queen first appeared with all her crazy moves it was nicknamed as "Scacchi alla rabiosa", madwoman's/rabid queen chess, and I think a crazy queen needs a mad king.. The changes in this variant are all about the king's ability to castle, while normal king movement remain as usual. I don't know if anyone already came up with something similar but here we go:
1. The king can castle with ANY piece/pawn in either vertical/horizontal directions (like a rook move).
2. There is no limit on distance so long as the space between the piece being castled and the king is open, a minimum of least one free square is needed to castle (can't castle an adjacent piece).
3. There are also no limits on how many times your king can castle in a game and it doesn't matter if the piece or the king have already moved before.
4. When castling slide the targeted piece until it's adjacent to the king and then jump the king to the other side of that piece like you do with rooks normally, so the king will always move 2 squares when castling.
5. You can't castle into a check, you can't castle out of a check and you can't castle through a check (the square the king jumps). However, the piece being castled with can be under threat or move through squares under threat without issue, only threats to the king matter.
You want 2 same colored bishops? Castle one of them. Your pawn is blocking an important diagonal? Castle it. Need to get a piece out of trouble? Castle it. The board is gridlocked? Castle your pawns and pieces around to try breaking through again. Or how about playing a stylish opening? 1: Play king's pawn forward. 2: Castle the pawn. 3: ? 4: Glory.
The king have truly gone mad.