I believe based on my research that as a daughter of a kohen, a bas kohen is expected to not tarnish her father and the whole kehuna’s reputation.
Therefore it is suggested that she marries a fellow child of a kohen or someone who is a Talmud chuchum ie someone who is up there.
Not that it is the case but if a bas kohen DOES do something wrong in terms of relationships – there is a more severe punishment then the average yiddenet