I've been using Fastmail for well over a decade (first signed up as xxx@fastmail.fm). I use the web interface for the very simple reason that it's just as good as any desktop app I've used and it's available without installation on whatever machine I'm on - even across Windows, MacOS, and Linux. It's not sexy at all, but it does what it's supposed to do consistently and without slowing me down. IMO there should be something to justify installing an app, and there just isn't in this case.
I do use the Android app, though. It has exactly the same "not sexy but works" feel for a platform where making a decent web app is even harder.