This. This is why.
At least browsing someone's web app using a real browser on a real PC, I know I'm in control of what data they do or (usually) don't have enough access to read.
I was looking into some of the new banks in the UK recently, and it is apparently becoming common to not only provide but require the use of their mobile app to identify yourself and set up an account with them. Oh, and by the way, their terms imply that they might also use that app to track a few little details, like your location at all times. Perhaps they just need "to make sure it's really you"? I will enjoy the Schadenfreude if the data protection regulator gets involved... but not as a customer of any bank that tries that!