The worst example I've seen personally was the pension plan provider at my current job. They required an app to sign up and manage everything. They don't have a web site and I was the first person to ask about it.
Parking in many places requires an app from an app store.
There's lots of small community things, local classifieds etc., that exist in niche things that only have an app. Like I said, trivial things, but they add up to everyday life becoming harder.
As for legal requirement: the government single sign-on that is used to interact with all government services and is also mandated for many important things like banks, insurance etc., is app-centric, though not app-only. They used to send one-time pads on cardboard but recently switch to electronic tokens. All government ID (for public health etc.) is also moving to apps. You can still get plastic cards, of course.
