Just a data point: Fastmail got them to implement/support push for Fastmail on iOS (no, it's not just IMAP IDLE).
Apple didn't have to build an API for them, they simply provided documentation for how to use the existing API.
https://blog.fastmail.com/2015/07/17/push-email-now-availabl...
But that's not the same as building a bunch of APIs for a competitor.