I'm curious what functions other than maybe depositing a check requires a banking app?
My charitable interpretation is that the app allows a greater verification process so the bank trusts it more and it's "to protect me, the user". But then, the website lets me transfer $100,000 using a multitude of other methods if I want (wire, e-check, create carrier check), so... yeah.
Edit: Not to mention that many of the newer banks don't even have web banking. It's app only. Of course, its your choice to open an account there though