my hospital trust had an enterprise-wide phone system with secure SMS and voicemail
Wow SMS and voicemail. The NHS enters the early 1990s. And that included easy to use, high quality photo messaging, and all client devices were photo-capable and to the same high standard for the troops as well as the bosses?
IME any corporate implementation invariably involves premium smartphones for the big swinging dicks, and the hoi polloi get to use some cheap shit that doesn't work properly "to save money". My employers (a c£7bn turnover UK operation) are not uncommon in this respect and expect the peasants to use Sammy Galaxy Ace 4's, which is a piece of unfit-for-purpose shit in a corporate environment. In fact, I wouldn't even give it to my kids.
I suppose this comes down to priorities. If I was in hospital, I really wouldn't give a tinker's cuss about medical staff using private mobile devices to seek second opinions, or communicate information about my care. If some ne'r do well hacked in and found a picture of my wound, symptoms, or care plan, I'd not give a shit.