Her premise of an accident is incorrect. I am surprised that no one has
mentioned it before.
In a model of 'There is G-d the creator' there is no such thing as an
accident. An accident is only possible in a model where there is no G-d -
everybody's birth is an accident and human existence is no more valuable
than that of a fly.
So, the reason she is not a cohen (and why she was born as who she was into
whatever conditions she was born into) is because this is a decree of G-d,
because this is the best thing for her to achieve whatever her purpose in
this life is. Now go and make the best of it.