How would that interoperate with the desktop thunderbird?
[1]: https://developer.thunderbird.net/planning/roadmap#firefox-s...
Presently if you aren't able to do any of the above something is not configured correctly. Some apps have differing opinions on where the sent/drafts/deleted folders should be for example.
The big integration points I see are within special features such as some kind of cross device PGP support, the ability to sync customised "from" addresses, and other features that the more basic built-in email apps lack.
Perhaps the code could be further extended to also support calendar, task, and chat functionality, just like on desktop, but that would take more effort.