I'm working on implementing this for the company, and the annoying limitations on iOS is that you can't clone apps. If you want Gmail (as an example) as managed app, you can't have another Gmail as unmanaged app. While the company can't see inside the Gmail managed app (without the app itself explicitly providing that feature), the company can remove Gmail (and any local data inside the app) at any time.

Fun fact from the MDM implementation - the most private way (at least to the company policies) to have a company-connected device is to buy a separate phone and install company's MDM on it. On company provided devices, the company may locate company's assets at any time but doing so on a personal device is a privacy breach.