“A Kohen is more holy than a non-Kohen”
Many factors go into ones “holiness”.
I think by saying that you are reducing an extremely complex topic to a superficial meaningless level.
A good example of something bad happening today coming from your train of thought would be a non-kohen rejecting the shidduch of a giyores for your reasoning when they could make a great couple.
Such belief and practice will certainly cause needless pain to converts and born Jews alike.