Yes, end-to-end encryption would fix all this, but it would also fix it in OP's satirical mail service, as well as in GMail - so that's really a tangential point.

Trusting that those providers don't start siphoning off a copy of your mail (or are indeed diskless and not out of malice or incompetence actually just using regular disks. Also, being diskless is worthless if they are still keeping your mail around in memory anyway) is no different than trusting Google to keep humans away from my email.