Castling in 960

As I understand, when you Castle in Chess960 your king and rook warp to the same locations that they would end at after castling in a standard game of chess.

Is there any particular reason that that methodology was chosen? I ask because it seems strange to me that you would shuffle all of the pieces around to create randomness, but then tie the rules of castling back to the positions of the pieces on a default chessboard. What would you think about a castling variation that is based on the number of squares that the king moves instead? i.e., if the king begins on the left half of the board it castles by moving 1 square to the left OR 2 to the right (with the rook tucking in next to it, of course), and vice versa if the king is on the other half of the board.

This seems to me like a more sensible way to do it than the current rule set handles it. What do you think?

(Edited to add paragraph breaks)

Personally I'm happy enough with the current castling rules in Chess960, although I know some players find them odd. I'd certainly consider other options, but haven't yet come across any that might be an improvement. Your suggestion is interesting, but it seems to me that a major disadvantage would be that if the king starts on any of the b/c/f/g files you're more or less restricted to castling on one side of the board only (since moving the king two squares into the centre wouldn't usually be desirable).

That same thought (regarding the king getting stuck on one side of the board) did cross my mind, but I just viewed it as an interesting quirk. Although I suppose getting stuck in that scenario ~4 times out of 6 might get old pretty quick.

The other option I considered when thinking about this was to just directly swap the king and the rook when castling. This would result in a lot of lopsided and/or absurd scenarios, though. Like the king traveling all the way from the b file to the h file, hypothetically.

Maybe look at it like this - where would you ideally want king and rook to end up after castling? Wherever the king starts, shifting it to the c or g file looks like the best option to me (and it's nice to have a little variety rather than the symmetry of b/g or c/f). That's probably what Bobby Fischer concluded too, hence the close connection to traditional chess. You could perhaps add extra castling options, and allow the king to go to any of the b/c/f/g files - what do you think of that?

I have moved my king all the way from the right side of the board to the c file by castling.  It can come as a shock to an opponent who is concentrating the attack on one side of the board to see the king basically teleport to the other side.  That's why the golden rule in standard chess to castle before the 10th move doesn't necessarily apply in 960.

Of course, the first time I played 960 I wasn't aware of the ability to castle, and I paid the price, big time.