Can we partially jaibreak our iOS devices for enterprise management?
Old question, and I'm sure you have answered yourself already, but I'll mention the Apple iOS management tool "Apple Configurator" (didn't find a good link for a tutorial).

It looks like you can lock down a few things.

One interest for "home use": it's the only way to lock down device pairing. Lets say someone wants the info on your iOS device. If it's unlocked for any reason, you just plug it into some device with iTunes, say "Trust" and now you have iTunes-level file system access (which is a lot).

LATE EDIT: Apple has mostly filled the “iTunes hole” in recent iterations of iOS. You need a password to pair the phone now, and iOS 11.4 seems to want a password every 7 days (much like TouchID requires a password after a bit of time).