Of course they don't enhance winning (unless you have Boise blue unis on their turf), but a recruit has never said, "Those matte black alternate helmets really made me take a look at another school."
New/Alternate uniforms provide fun for the kids, publicity for the athletic department, and hopefully some revenue in merchandise sales.
In the big picture it may marginally help, or I am sure you could "prove" it doesn't help at all, but it sure as hell doesnt hurt. I can't remember if it was you who brought up the budget issues, but if you really think the reason we aren't doing alternate uniforms is we cant afford them, that's very silly of you.
Uniforms are an afterthought when it comes to the kinds of money the athletic department deals with.
How much would two full sets of alternate uniforms cost (pants, jersey, helmets)?