In the scenario you describe above, the unencrypted contents of your email are now generally stored on at least 4 machines (maybe 3 depending on what the recipient's POP settings are), with only one most likely being under your control (the client you wrote the mail on).

The benefits of encrypting the message as well as the transport are mostly for dealing with that fact.

Yes. The adversary is assumed to be global here and so it can listen to the traffic at both ends. Also, both servers can make copies of the email.

PGP gives you end-to-end encryption, which starts from your computer and ends at the computer of the recipient.

If the SMTP server relays your message in plain text, isn't it vulnerable to snooping in transit?

you generally only know about the crypto on the first smtp hop. SMTP crypto is fail-open, unauthenticated and not end to end. it's transport only, decrypted on each SMTP hop.

What about your respective SMTP servers' disks?