One possible reason is that the planner configuration can be different per connection, so the plans might not transfer
I believe the plan data structure PG is intimately tied to process space memory addresses since it was never thought to share between them and can even contain executable code that was generated.
This makes it difficult to share between processes without a heavy redesign but would be a good change IMO.
> One possible reason is that the planner configuration can be different per connection, so the plans might not transfer
That's part of it, another big part is that the transactional DDL makes it more complicated, as different sessions might require different plans.