For the longest time I was using Google Apps via Exchange with the mail.app. I tried icloud.com mail a few times but it drove me nuts to see unread mail notifications on the lock screen when I had read them on another device.
In 2015 I came across Fastmail. Such a good mail provider. Ability to host multiple custom domains and all sorts of advanced stuff. I think they worked with Apple to get push working on IMAP a few years back. What I really liked was that I could use custom domains, get live/push for new mail, read status, moving/deleting and flagging on both iOS mail.app and macOS mail.app.
There was a thread running for a while with discussion around it:
A guide to using iCloud email with your own domain name | MacRumors Forums
[doublepost=1496799646][/doublepost]Also on this topic, I’ve been wondering recently (was curious about iOS 11 but maybe in the future) if Apple builds a new mail app that becomes more proprietary for it’s icloud.com mail service and brings a lot of new features to it. Kind of like how Notes has grown after breaking it away from the IMAP protocol. There’s been a lot of creative ideas with different 3rd party mail clients, though I guess they likely are used by a very niche set of users.