The FBI decides they'd like to read that conversation. They issue a court order requiring you to hand over your TLS private key, and use it to MITM your users to feed them corrupted JS code that discloses PGP private keys.
The small minority of users "detect" this change. But not quickly enough: the whistleblower has already logged in to check their mail, and has now disclosed their private key to the FBI.
What now? What's the feature you're going to build to keep that from happening?
Not only are you using Javascript crypto to provide this "service" to users, but you're not even forward secure.