Once you've used a service like Intercom, FrontApp or even Google's "Inbox" you realise emailing can be far more productive. It's a shame that companies like FastMail gave up on trying to improve the experience.
The features you list sound like something that should be implemented by an email client not an email host. I realize they have their own client, but that is really just a means to an end as it is obviously not their core business.
On top of that, it sounds like you really want something other than email.