I looked into this some time ago, and to the best of my knowledge, the "$" has no legal meaning as far as Fedgov is concerned. A "dollar" is actually a unit of weight. (416 grains of silver) This is a historical oddity that comes from the fact that the Constitution specifies that gold and silver be used as a unit of currency. I'd be interested in knowing if they made relevant changes to legislation in recent years to make "$" = "dollar".
Very interesting. My gut feeling is the reason for spelling out the value has to do with artistic concerns. Some US coins from the 1700s & 1800s did have numerical numbers on them. Without doing some research, I think the last time this happened was in the mid-1800s.