What does specialized to the process mean? Lots of JIT tooling these days readily supports caching and precompilation. Invalidation is hard but things like reloading global references are hardly intractable problems especially for an org as large as pgsql.
Pointers to process specific memory addresses to functions other data structures that only exist in that process. I didn't say it was intractable only that it takes more effort, other databases do it.
The current PG query plan and jit is designed around just being in memory in a single process, this would need to be extracted into something not process specific and shared between all processes. The plan itself is just a bunch of C structs I believe.