I mean, there might be a point if we only had S5/S6 to go off of, but... I wouldn't actually expect her to reallydo aterribusle with her authority, or using magical power recklessly, by the point of S9. She does seem quite uncomfortable with the idea of time travel, "[in any case.":](/images/2144366
)
Whether she'd actually want to be a _*Princess_*, is possibly a good question, though, because she has absolutely nothing against following Twilight's lead, or helping her live up to what she believes in (S7, S8). Sure, she got past the hangups she had regarding leadership, but... would it be true to the degree that would be on that scale?
(I think Pinkiecorn always did fit far better fintor that tag, to be honest.)