Is it possible to track installed apps usage on iOS devices using MDM profiles? I need to track not enterprise distributed apps, but all other apps installed on the device.
I need the information on when each app was launched, and for how long it was opened.

As I see so far, it is not possible, but maybe I am missing something...
I think your conclusion is correct. This information is not included in the MDM Protocol Reference and therefore isn't available through MDM.

The only way I can think of would be to side-load (using an Enterprise Distribution certificate/profile) an app that uses private APIs to monitor such activity and report back. Not recommended and against the Developer Program T&amp;Cs I believe...