The summary is wrong: The issuer does appear in MS Authenticator, if the QR code is properly implemented. I can see Amazon, Login.Gov, etc. listed.
I have one site that has the issue (Payrix). All of the other sites I use work and appear fine in Authenticator.
The Payrix site works in Google Authenticator but simply shows my email address as the login; I assume I'd have the same issue if I added a 2nd site with the same email.
I agree that Microsoft should make it more difficult to overwrite existing settings, but these sites have some responsibility to make sure their QR codes work correctly.