I am not a cryptographer. Maybe that is why I don't see the issues with integrating PGP into SMTP.

In my head: Lea requests the server of Luke's domain jedi.com to tell her the public key of luke@jedi.com (The request includes an encryption method perhaps). She gets back the key PUBLIC. Then she encrypts the message and Luke can decrypt it easily.

It's not that hard, why isn't it standard for years?


  It's not that hard, why isn't it standard for years? 


Because that would not have solved the problem that PGP is trying to solve. 

PGP is an end to end encryption, so if there is any way for the SMTP server to subvert the encryption, then the scheme fails.

In the case of the scheme you proposed, suppose Alice (alice@charlie.com) wants to send a private message to Bob (bob@dave.com). Using the scheme you proposed, Alice's mail client or Alice's SMTP server fetches Bob's public key by making TLS connection to dave.com. This is fine as long as dave.com are honest and actually return Bob's public key. But dave.com could have been configured by dave.com's operator to return a forged public key created by Eve, or Eve could hack into dave.com and set this up. Now Alice's mail client/mail server would happily accept Eve's certificate, thinking the public key is Bob's. In this model, the operator of dave.com can intercept any of Bob's emails.

Now, as long as dave.com is honest, this still protects against third party spoofing. Why don't we do this anyway if this protects at least against third party snooping? Mainly because SMTPS also provides the same level of protection, while also being much simpler. If MITM by the mail server operator is not your concern, you can already very well secure your emails by ensuring you both uses SMTPS.

Note that the difficulty of end to end encryption isn't about fetching public keys. Most email client that supports PGP also supports automatically fetching public keys from LDAP or HPKP. The difficulty of end to end encryption is verifying the public keys. 

There is no known method of verifying public keys that is fully transparent to the users and fully secure. Web of Trust or Certificate Authority model comes closest, but Web of Trust comes with a lot of caveats and Certificate Authority model relies on a third party to do the verification.
