Isn't cholesky - used to substitute householder at a point - faster but less stable in some cases? I'm just recalling from memory since I had done a small project on qr decomposition with householder for an exam this year. I mean, if it is faster than the standard torch operation probably there are good reasons for which it is not the default standard torch operation. Might as well be wrong, I'm not sure

For once Cholesky is less general than QR: Cholesky only makes sense for positive matrices, while QR works for any matrix (including non square).

Also QR is a primitive for operations like finding eigenvalues, and I don't think Cholesky can be used there.