Re: Does it make sense to send encrypted e-mail?
No, it does not need to be double-encrypted. If impersonation is a factor (and it may not be), then your message is simply *signed* with your private key, not double encrypted. i.e. a hash of the message is encrypted with your private key and appended, not the entire message.
In some circumstances the recipient will not have your public key, so double-encrypting in the way you suggest would make it impossible to open.