The examples I can think of are:
- Covid apps, which makes sense because you can't quite do contact tracing using a website and people would trust some corporation less than a government. They're completely optional and it's temporary. The download count is less than a third of the population where I live (and I got it on both of my mobile devices so... extrapolate from there).
- Germany uses a proprietary app that requires Google/Apple services as replacement for emergency broadcasts. (In NL this is also being moved to mobile, but using broadcast SMS so not a special app.) Not sure if there are any official goals in terms of install rate, but nobody expects near 100% and it's not compulsory in any way. I'm honestly not quite sure what their goal is because I'd guess the install rate so far is a few percent and it's not being promoted at all.
A lot has to be done digitally, ask any grandma in the Netherlands what hoops she jumps through or has her kids do for her, but every time something new comes up, there is a lot of talk about keeping things accessible. Very few things are mobile-only (these "requires time-sensitive notifications" type apps mentioned above are the only ones I can think of), and only slightly more things don't have an offline fallback. So far, of course. I expect that we'll move more towards digital with (by 2050) a few help stations for the people stuck in the 2010s, but (de facto) compulsory closed source software that needs to be running on a body-worn device? Given the amount of discussion already surrounding the optional open source covid apps... I don't see that happening too soon in democratic countries.