I hadn't thought of this use case for aliases.

I had to make my Outlook email primary again on my Microsoft account, unfortunately, because of how I use OneDrive. I send people share invitations and there are scenarios (or at least there were the last time I checked) where sending invitations from the primary account email is the only way to deliver the invite. If your external email alias is primary, they'll attempt to send an email from Outlook's servers that spoofs the alias email :/

I just tested it, and it looks as if that was fixed. It seemed to work for me.