As I understand it, PGP uses RSA just at the outset to generate a 128-bit (or 256-bit or whatever) key for the rest of the message. So the PGP key length is a one-time cost (per message).

Many years ago (early 1990s) I generated a 1024-bit public key which was the limit at the time. A lot of Moores have passed since then. Since key generation and usage is no more than O(bits^2), possibly only O(bits log bits), I don't see why people aren't creating >= 8192-bit keys these days.

Or maybe they are. The MIT keyserver is down at the moment, at least if I ask it for anything.