Why database diagrams are not working when domain account is attached to database owner?
You don't need to be sa or another sysadmin account to create database diagrams, but I think you may need to do this in order to initially install database diagram support.

If you do this as sa, you should then be able to let domain\username create diagrams. Most of the resources online will tell you that if domain\username is the database owner it should work, but there is a slight difference when you just set a login as the owner of a database and they aren't already a user inside the database: they get mapped to the special dbo account. I seemed to be able to do this in SQL Server 2012, but I used SQL accounts not domain accounts. So I don't know if that's what is causing your issue, but I think I have provided a valid workaround.