>if an employer demanded I install an app on my personal phone, I'd refuse.

I did that once. In very polite terms I told them that I like to keep personal and work activity separate as much as possible for personal and work security reasons and that if they issued me a phone with an app I'd be happy to carry it.

I got a very positive response. Ultimately they didn't think it was worth issuing me a phone and everyone went on happily.