Enroll in to device management in Windows 10 not possible

In Windows 10 operating system (on both Mobile and full OS) the following can be done: Enroll in to device management. This on both domain-joined and non-domain-joined devices, where no ConfigMgr agent is present. When trying to enroll a new Windows 10 device however, the following message is displayed: System policies prevent you from connecting to a work or school account. Contact your support person for more information.

This because the account logged on has not enough permissions. Trick is you need local or domain admin permissions for it.

When logged in with local or domain admin permissions, enrollment is available as expected. When enrollment is done the following message is displayed: Well done! You're connected to work or school.

When logged in with user permissions again, enrollment is still not available. This because the following message is displayed: Another user on the system is already connected to a work or school. Please remove that work or school connection and try again.

If you ask me, I find all those messages bit of misleading. Why not mentioning you need special permissions for enrollment, instead of showing that system policies prevent you from connecting to a work or school account? That will help for sure!

Hope this will be more clear in a future release.

Source which points me to the solution: Kevin Kaminski's Virtual World