@Mr.Toilet
3 out of 4 are from noble families, as for the one that is a commoner, I'm pretty sure she is related to the noble family of her palace but isn't an official member of the family (an illegitimate child). Besides, despite being supposedly a commoner she is still considered to be a genius that was accepted by the palace, which means that she has political weight due to her connection with said palace.
As for how deep the author's understanding is, it's hard to judge based on manhwa. If I'm not mistaken this is a manhwa adaptation of a novel, and it's a well known fact that such adaptations usually cut out a lot of context to move the story forward faster.