...the problem is not the encryption of messages you are sending, but the automatic decryption of messages you receive (and for which your private key is needed). Since different clients and protocols are affected (not just PGP, but S/MIME too) it seems this is not just a problem of the implementation, but a conceptual problem (this is why I wonder if other end-to-end encryption might also be affected). Let's wait for more detail on this.

One reason clients like Enigmail were developed is that many people find the traditional encryption and decryption process in PGP too cumbersome and are confused by the whole public/private key business.