Archiving for distribution and backups are very different things. You don't care if some app distribution compressed file gets corrupted, you just compress again but your compressed backup files usually don't have much source of reference.

I wouldn't use any unreliable format for backups. I picked bzip2 for stability and compression rate.

In my opinion, the compressor is not the right place to add data integrity mechanisms, especially since data integrity mechanisms only really apply to particular media. Data on hard drives don't get corrupted in the same way as data on TLC SSDs, and generally on the latter you're better off with redundancy and diversification, than with inline error correcting codes.

Honestly, I don't see why xz should have any of its own data integrity mechanisms whatsoever, except maybe a whole-archive CRC32 or similar.

Right. The purpose of an archiver/compressor is to store a bunch of files together, and use as little space as possible to do it. Data integrity / error correction / redundancy all lie in the opposite direction of that goal.