In Bioware canon, demons can possess cats, nobody can agree on how lyrium works, Grey Warden's ability to sense the taint is only remembered when its important to the plot, an elven god hangs out in the body of a human, and BloodMageSarcastic!Hawke is the Champion of Kirkwall, not "dirtbag who ruined everything", so I don't understand why CadashQuizzie is a particular hill anyone wants to die on, shrug. These games are a mess, they have always been a mess. They're a fun mess and I love them, but they're a mess.
Why on earth do you think it's unbelievable they can harness the power of the anchor when we weren't even given enough information about the anchor to know what one needs to do to wield it anyway? And it's not like Cadash was all YEAH MY HAND MAGIC LOOK AT ME, Solas is the one who stabilized it and told them how to work it.
By the time Cadash is made leader of the Inquisitor, they're a religious icon who faced the big bad, "died", and came back and no one cares about their background anymore. It is very very clumsily implemented, I"ll agree, but I think it is across the board, not just specifically for that. Shrug.