Exactly why I use Fastmail. AFAIK, it's the only email service that supports iOS Mail push notifications properly.
It's actually quite magical, in fact. It's so fast that as soon as I read a message on my MacBook or iPad, I can usually see the notifications disappear from my Lock Screen on my iPhone sitting beside me.
Honestly I agree. I had been trying so many services and nothing came even close. I remember being amazed at how it somehow managed to check every box. I was quite happy too when we got coloured flags a few years back in the iOS update and they synced properly to macOS Mail.
I do really hope Apple brings this to iCloud Mail. I've always been perplexed that it hasn't been there since the beginning, but then again I come from a pre-iPhone era when Blackberries roamed the earth. I feel like most people don't care about these things nearly as much (as evidenced by the number of people I know who have a four-digit number persistently hovering over their Mail icon 😏).
100%.