Re: But what about...
The same way he would now.
That could only possibly work for a small subsection of the encryption that goes on, then.
Currently, Alice will encrypt a messge with Bob's ublic key, and he will decrypt it with his private key. For Alice to send the decryption key with the message - she would need Bob's private key. That means it's not private any longer.
You encrypt the stream using a session key
So your system can only possibly work in a mechanism whereby a symmetric session key is negotiated between the endpoints. That cuts out the bulk of such messages. It also means that - were one to want to do something nefarious - it would be trivially easy just to send something other than that session key as the purported decryption key - which would only be discovered much later, when the transmission is decrypted by Law Enforcement. Thus it will be a hindrance to people going about their normal lives, but won't touch anyone who is prepared to fake the session key. And if someone's happy to blow up a building, I doubt there'll be much compunction over lying about a decryption key.
TL;DR: your mechanism is, like so many others, entirely useless when it comes to law enforcement, despite requiring significant intrusion into the private lives of innocent people.
Vic.