Yeah, Apple doesn't support IMAP-IDLE which is a drag, so push is out. And you're right, there's no calendar. I also hear LDAP is read-only on devices, so you can't add to your Fastmail address book from your iPhone.
I personally don't use any of those things anyway but I can definitely understand why that would be a dealbreaker for a lot of people. It's great for email and the webmail interface got way better recently. Their blog is also pretty neat, they go into a fair bit of technical detail about new features and how they solved certain bugs: http://blog.fastmail.fm/2012/11/26/inter-tab-communication-u...
I closed my google account today after spending a few weeks migrating. Try fruux for calendar and contact sync, it's hosted in Germany and I'm happy with it
