I think the description of REST you've outlined is not entirely right. The statelessness relates to client state, not the system state - i.e., POST/PUT/DELETE etc. can very well change the system state and that's the whole point of them - and also session state is allowed too, it's just not the part of REST architecture but is assumed to be implemented externally.

It is true that HTTPS may impede some cacheable resources. Maybe HTTPS may be improved to allow transparent caching of _some_ content, but the security implications may be hard to predict and will require very careful implementation to not introduce new security issues with attacks on caches themselves (DNS system still has this problem AFAIK).