IMAP is awesome, but has some rough edges around things like IDLE being only able to monitor one folder per connection. This means users may get an inconsistent experience depending on the number of folders they have, with emails arriving in some showing up immediately, while others have to wait until the regular "check for new messages" check.
JMAP (for example) removes these problems, and for mobile applications, provide a better experience.
https://en.wikipedia.org/wiki/JSON_Meta_Application_Protocol