Well, yes, but also, that angle works a lot less when you try to pull it off.in fantasy, since magic and impossible things are possible.
Also, shes a royal princess, it'd make more sense to make her an underdog, if she was a commoner, not someone who's already one of the highest ranks amongst the kingdom.
What you're saying isn't really wrong, but the reasons and methodology people try to bring her down a peg, just feels so contrived. More so for the sake of having a plot, than for making thematic sense.