Originally, Windows 10 supported users syncing their Edge Favorites across devices via their Microsoft account, even to a computer connected to an on-premise domain but this was disabled in one of the Windows 10 updates. Microsoft made the ridiculous claim that this was in response to requests from IT pros. I don't believe that claim, because we would always ask for a Group Policy for something like that, never a blanket change.
With the advent of Timeline with the 1803 update, this appears to suffer the same fate -- useless on a computer connected to an on-premise domain. Just no way to sync for those computers.
This is so bad, because it drives our users to avoid using the Edge browser (because they can Sync if they use the browser-sync in Firefox, Opera, or Chrome) and destroys any ability to leverage "use the same OS at work and at home and benefit for it." As a Microsoft fan, this is infuriating to me, both as a user (who desperately wants to sync my own personal systems) and as an admin, watching this alienate other users and lead to strong anti-Microsoft sentiment.
It has remained my hope that Microsoft would fix this tragic, self-inflicted stake to the heart of Windows personal usage with a subsequent update. Now that Windows 1809 has shipped and Server 2019 is available for testing, is there any evidence of Group Policy settings that we admins might be able to set to allow users to sync their Edge Favorites or Timeline on a computer connected to an on-premise domain?
Colin