On the flip side, the ability to look up your past purchases can enable returns without receipts.

The other week a store clerk failed to look up my purchase when using my physical credit card, but succeeded when using the same credit card via Apple Pay. I would have been out of luck if I had rotated my Apple Pay number.

Or perhaps your device could store previous identifiers and offer those to the vendor to lookup in their system? Assuming the vendor isn't doing something shady like building an association table between identifiers, this would preserve your privacy and let you change your identifier as much as you like.