Here’s a great article by Dave Wiskus:
I heartily agree with this paragraph. I think this problem is being made even more manifest because of the push toward flat design, since there are fewer elements besides typography that can set an app apart. Textures being a thing of the past, you’re mostly limited to color, fonts, and animations. But if you’re trying to give your app a certain feel, your efforts can be seriously hindered by something like a UIModalAlert appearing in Helvetica Neue.
I may or may not be starting work on a top-secret iOS app in my free time. Picking fonts is an important stage, since it’s going to play a big part in defining the look and feel of the app. Using Helvetica isn’t an option for my purposes. This is because its letterforms don’t breathe enough to accommodate comfortable, prolonged reading. Helvetica is good for a lot of things, but it certainly isn’t great for everything.
That said, Helvetica is about as generic a font as you can use. It’s used virtually everywhere, which means most non-designers don’t even think about it when they see it. If I had to pick a font to interrupt the immersive experience in an app, I’d probably choose Helvetica.
I still agree with Dave Wiskus, though, and would say that Apple ought to let designers have control over all the typography a user sees when he’s using a given app (except the Notifications Menu and the Control Center, since those aren’t a part of the app and should thus feel different for good reason). This will help those who make apps to create and enforce a feeling for their app, which is what Apple says design is all about anyway.