My bank offers both an app and a website which is nice, but the app is mandatory for doing any kind of operation involving money (which is not that uncommon when logged-in in your bank accounts ;) even when connecting through their website, as the app is used for some ID-ing process.

Then, there are a few not-mandatory but such-an-effing-pain-to-not-use apps, say to ID oneself with some (public) services.

I use a dumbed down iPhone (like, really: no social, no games, no whatever not even email is configured on it) just so I can access those few apps.