There isn't a widely used transport layer standard for OpenPGP, which is what the protocol needs, so TLS is probably a better choice then PGP for the actual encryption.
This is very much false, all information could be encrypted using the public key of the user that wants to send the bitcoins and then decrypt by their machine. Also I wouldn't include gpg into the actually bitcoin client I would have it called out to the shell so their is a disconnect of passwords and stuff.
No it's not false. TLS (per its name) happens at the transport layer. It's baked into every http library in the world. There really isn't a standard to do this for OpenPGP that anyone uses or is supported by any library. What you're proposing requires everyone to implement an ad-hoc poorly specified made-up-just-for-bip-70 encryption scheme and shoving it into the presentation layer.