They're a pretty bad stopgap: https://bas.westerbaan.name/notes/2026/04/02/factoring.html. Going to RSA-32000 only buys you ~a year once QCs can factor RSA-2048. In order to get a standard that would resist quantum attacks for realistic time, we would need MB to GB keys at least (see https://eprint.iacr.org/2017/351.pdf for a hilarious post-quantum RSA attempt that used terabyte size keys)

No, and even if we could, it would require a migration of approaching the same difficulty of a migration to PQ, at which point why not just migrate to PQ