Why are the symbols 0-0 and 0-0-0 used for castling in algebraic notation? I'm curious about why the symbols O-O and O-O-O  are used for castling in algebraic notation. Why not use the consistent and logical Kg1/Kc1 for White and Kg8/Kc8 for Black? Why adopt the less than obvious O-O and O-O-O from descriptive notation?
The castling notation was invented by Johann Allgaier and used for the first time in his 1811 2nd edition of his Neue theoretisch-praktische Anweisung zum Schachspiel.

He didn't explain why he came up with it.

Allgaier (and algebraic notation in general) used digit-0. The use of letter-O is an anglo-saxon oddity.