For message relaying, your proposal might indeed work. The vast majority of inter-domain mail traffic goes through a very small number of providers. No mail provider can afford to not be able to exchange mail with gmail, or office365, or ...
It is trivial to set up a mail server with TLS and if you don't have fucking TLS bounce it through a protocol upgrade server. If you understood the type of secrets that are getting trivially intercepted you'd realize that a couple hard days for a couple of lazy sys admins is a tiny price to pay for the drastic increase in security.
People are literally getting killed because we're so fucking lazy. Even three letter agencies are sending mail without TLS, this is madness.
Anyone running that mission critical hardware is free to keep using insecure email, no one is going to stop that. If they really need to send email from that old hardware to gmail, they can set up their own relay that accepts non-tls connections but relays using TLS.
What the big sites can do is add a delay when receiving from a plaintext relay, in a manner similar to greylisting and tarpiting that are widely deployed. The mail is not rejected, just delayed. The delay can be proportional to the amount of mail sent by a domain, and set to increase in time. The same can be done for outgoing mail to domains that don't advertise STARTTLS, drop the connection and retry later.
In the first phase, just issue a warning then drop the first submission attempt, to fillup the logs with a clear message that STARTTLS is strongly preferred. Gradually increase the delay so that large sites have trouble emptying their queue, and continue to increase the delay until the last holdouts can be simply shut out.
The advantage with this approach is that the user of Gmail, Yahoo etc. does not see a problem with his account, while the smaller sites and users will have delays when sending mail and receiving mail and be forced to take action.
It's essential that the major email domains work together so that the users of small non-encrypting domains feel a generalized performance impact, not just a problem with Gmail or just Yahoo.