It looks like there are no laws that restrict US companies from prohibiting romantic relationships between co-workers. (In reverse: US companies are allowed to prohibit romantic relationships between co-workers.) The practicality: If you did restrict it in employee rules, probably people would do it anyway in secret. It is better for HR to know so they can make sure there isn't a supervisory conflict.

If prohibited and they do it in secret, then you have a free fireable offense in your pocket. Some employers like to have a stick ready to use on a whim.