In practice, the money goes to the girl's father. This can lead to a very bad situation if the girl backs out of a lucrative marriage, and may be the cause of many "honor killings"
Keeping marriage in the family/tribe keeps the money in the family/tribe.
It also explains why Muslim men want to convert Western women to Islam: no bride price required
American need to learn this in case their foolish daughter hooks up with one of these Muslim's shopping for a western woman. The father should demand a largwe dowry that the guy couldn't possibly afford. That would put an end to that relationship, and saving their daughters from a life of beatings and misery as well.