I had a similar experience. I couldn’t add the AmEx Plt Edge Supp card to my main account and had to create a new login for it - this was a couple of years ago.
I got a AmEx Qantas Premium Supp card a month ago and it added to my main account just fine.
As far as I can think of, it is either the card type or the relationship with the primary card holder that makes the difference - I asked the AmEx CS on this and their thoughts all supplementary cards need their own logins and she was surprised that I could add my new Supp card to my main account.
Just remembered, my wife could add all her Supp cards to her main account…seems like no logic there.