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I've always had this "outlook_string at outlook com on behalf of the desired email address" behaviour - both before and after the upgrade to EAS. That's what I avoided by using Linked Accounts. However, now post-upgrade, Connected Accounts don't save sent items in the Sent Items folder so I tried alias again in Outlook.com and it's still the same. "on behalf of" doesn't cut it when using it with sites expecting your desired email address and/or clients who know you by desired email address.
And, as it happens, I have an inbound email from a correspondent to whom I have previously sent from an alias - in her reply to me, you can clearly see the "on behalf of" nonsense I don't want:
If they hadn't broken Connected Accounts Sent Items folder, this wouldn't have mattered. But they did. Now, there is no way to use a non-Outlook domain with Outlook and have your outbound emails a) look as if they come from your domain and b) get saved in the sent Items folder.