As requested by some working councils in Germany, SMC EAS Proxy can be used to block e-mail delivery after the working hours. Sample: E-Mail to mobile devices will just be send 7am-7pm. After 7pm mail delivery will be stopped via EAS Proxy. The profile remains, no mail will be deleted

Implement a backup functionality, which uses the phone owners dropbox or other cloud vendor account. The data remains in the hands of the user

For loss/theft protection, please implement the ability to let the phone ring in a very loud tone (even on muted) for at least 1 minute.
This helps, if you have lost your phone in your house. It also can disturb thiefs to get away unnoticed

The app should give the user some feedback for all files updated in the cloud. This can be either a continuous log or a opup windows

Instead of whitelisting/blacklisting specific apps, why not be able to allow/block certain categories of apps instead? So that you are able to block games but allow productivity apps. Trojanized and malicious apps could be blacklisted as default.