I think that is why annulments are in a sense easy to get. It is rare for a wedding to lead to a real marriage. When the church says that it doesn't believe in divorce, the cause and effect are backwards, by its nature, a marriage is insoluble.
The same applies to priests. When people say "let them marry" well, they wouldn't be priests. The idea of a man so devoted to obeying a higher ideal to the exclusion of worldly ties predates the church. The mystic has always existed.