This is about Outlook.com not other apps or accounts. Currently there is no way to remove already synced 3rd party accounts. It looks like somebody simply don't want us to remove any synced contacts. It's all about that privacy crap and who will snag from
whom our contact list. Earlier it was possible to sync all your contacts between all accounts without problems (Google, Facebook, Yahoo, LinkedIn etc), but then Facebook got in power and they cut the cord. Now Microsoft in fear to loose all already synced
contacts, they just block any options for us to control our own contact list.
How is it by Microsoft Privacy Terms and Policies? Everything what is synced to their servers - does it belong to you or them?
The only solution to this marasm I see is to completely delete Microsoft account and create a new one and restrict any kind of contact/account sync.