I am annoyed by this too. The big limitation would have had you could not use IMAP as that is remote.
The other issue is implementation. It would be easy to forward or attach or just store unencrypted in an insecure way which may not be desirable. Frankly for what I do I would prefer Thunderbird decrypt on receipt but place all content in a vault. If one wanted to add some more restrictions one could make it hard to forward by accident mail that was originally encrypted.
The big issue with PGP has always been a combination of bad implementations and key distribution.