Even for hosted email, it would violate most corporate infosec policies.
It never occurred to me that installing "Microsoft Outlook for Android" would mean "upload all your hospital email to some acquihired cloud". When Google abandoned the Email app in Lollipop and forced us all to add our Outlook accounts to the Gmail app, I was concerned (Google does explain quite clearly that this is just a UI thing and that it's not merging the email into the Gmail servers at all) that I would have to go back to those abominations in the Play Store since all the Outlook clients on Android suck and K9 refuses to work with our Exchange server. And here Microsoft releases Outlook for Android and I was all excited for nothing.
Thank god I didn't receive any emails containing PHI while I had it enabled.
It is so extremely frustrating to have to deal with a corporate Outlook server on Android. That's why I was excited that Microsoft finally put out something.
For all the horror stories of corporate IT lording their position over people lower on the ladder, in the end they are a service organization that is reacting, not dictating, and in this case it's often the executives who get the expensive-at-the-time tech first anyhow.
Anecdotally I've seen IT teams having a much easier time explaining why you can't forward everything to GMail, for instance. That chimes with quite a few reports coming out claiming European-based cloud hosting is benefitting at the expense of US-based setups.
BYOD is still a real thing, for sure. But iOS talking to corporate Exchange can relatively easily be made compliant with infosec. A third-party app ingesting corporate email to servers hosted in China under vague licensing? Not so much.