"Most people don't know much about Alexander Hamilton, so it's easy to treat the show as a kind of expanded School House Rock, particularly since it's based, notably, on an extremely in-depth and well-received biography (which itself has been accused of hagiography). Everyone wants to be an expert."
Learning specifics like that they had brothers and that Anjelica was already married at the time does change my perspective on Hamilton. I don't suddenly think it's a terrible show but I think as you said, there's an idea that this musical is illuminating stories of historical figures that aren't often told so these kinds of inaccuracies for the sake of drama are a little deflating. Satisfied is still a great song but the impact is lessened.