Is it possible to be attractive to many, but desirable to few?

In my life I have come across many different looking people. People many would say are very attractive, good looking, average, or other. What I have found interesting is that despite their so called “attractiveness” some people just have a natural desirability factor. I’ve met attractive people who have great personalities, social skills, good hygiene (lol).. and who are constantly told by others/strangers they are attractive. However, they have the hardest time getting dates. While there are others with the same qualities, but their “lil black books” are full! What is it? Can you be attractive to many, but desirable to few?