A few thoughts:
1. I don't know if HTTPS is the best analogy, since it took 20 years for it to really become widely used (vs. non-secure HTTP). I think a better analogy might be the transition from HTTP/1.1 to HTTP/2 (or HTTP/3?).
2. I don't think we can rely on large providers (e.g. GMail) to quickly adopt a new system and even issue switchover ultimatums. A simpler mail system may not be in their best interest. Aiming for slower, organic growth could be more realistic. Even if a next-generation mail system never becomes dominant, it could still provide value. (Maybe Mastodon/ActivityPub is the analogy here?)
3. In any sort of reboot, I think a modern encryption system (something like Signal protocol?) would be a must.
4. Can we have a system where senders need to hold tokens to authorize them to send a message to a recipient? The whole "anyone on earth should be able to send you an unsolicited message" idea is ultimately the source of the spam problem. Messaging systems that rely on bidirectional agreement have much less of a spam problem. (Obviously this raises a slew of other technical and UX questions...)
I know that making too many changes is a risk. But I think that there is also a risk in making too few changes. (If the value proposition isn't sufficiently bold, this may hurt adoption.)