As a kohen, I can say that just like everything else in life, each plus has its minus. A kohen has its advantages by being a kohen, but there is a disadvantage that you cannot marry certain people.
I can say from personal experience while dating, that there were people that I wanted to date and thought would be compatible, that I was unable to date because either they were giyoret, or had other issues in which halacha is clear that I would not be able to marry them.
Especially older single kohanim, do not have it easy, because for whatever reason their pool of available older singles is much more limited.
For anyone to say that a kohein is lucky to only be able to marry a besulah is a totally ignorant thing to say, and one that lacks compassion for kohanim trying to get married and follow halacha.