I use PGP every day. Who messages me, how often, and at what times, is still private information and I should have a say in where and how that happens. My PGP-encrypted conversations tend to be much more sensitive than any other medium I use.

The cryptography is almost certainly not broken. That does not mean it won't be broken in the future. I would have the same concern if my TLS-encrypted traffic was being saved. If my ISP was saving TLS traffic or my XMPP provider (the one that I don't host, anyway) was saving OTR conversations, I would be equally concerned.

Even worse, actually. TLS (usually, nowadays) and OTR both employ forward secrecy. PGP does not, at least traditionally.