I share the dislike of everything needing apps these days. The sony one was a little bit annoying because it seemed to have some paid products looking like normal features. It also occasionally turns on a feature that was quite annoying, where talking (even clearing your throat) would turn off noise cancelling and even amplify ambient noose. And I had to use the app to switch that feature off once a week.

The Momentum 4 works well without the app. It's nice if you want to change the equaliser settings. I sometimes do as they have a preset for audiobooks/podcasts. And it's been nice to confirm the effect of gestures you can do on the headphone (most moderns over the ear headphones have capasitive finger gestures on the flat side). Bluetooth works fine out of the box, and with it you can check battery power, switch tracks, volume, all of that stuff.

The only thing you really need the app for, is updating the headphone firmware, which you likely want to do, as they sometimes improve the notice cancelling, etc. Sidenote, that update took almost half an hour to complete, which is the longest firmware update I've ever seen. I havent checked if it is possible to update firmware using a computer and USB.

In any case. If it helps you out, I'm glad. Have a good one.