Yes, I use their calendar web app on Desktop (the one next to Mail). For mobile, I sync individual calendars into my Android Calendar ("CalDAV-Sync").
My biggest issue with the Google Calendar was the syncing rate of 24 hours for iCal feeds. On Fastmail, new events appear quite fast (and I can force the update manually, if I need to).
This seems like a really common use case that ought to work well. I switched to Fastmail a few months ago (I still haven't fully committed to sticking with it.)
Did you contact support?
Did you solve the problem by switching to another calendar provider?
I use their calendar with various apps like Fantastical or Timepage. It's standard CalDAV and should work with any decent calendar app, including defaults like Apple calendar.app.