I think a lot of them agree to any couple getting married even if they arent believers, dont tell them what to expect or how to behave, as long as they pay the marriage license fee. Most people decades ago, would get married in a church and then would never attend again until someone in their family dies for the funeral. They want to the ministers blessing but they dont eant to have to obey or do anything further with the church family that they supposedly married into.
There are judges for that sort of thing now. But if the preacher does marry a couple...let's say they are both virgins, their parents consent (more likely 200 years ago)... and the clergyman marries them. At least they aren't shacking up. If clergy don't want to see society shacking up, then performing a wedding prevents that.
Performing weddings is a 'cultural duty' of clergy, not a Biblical one.