I don't know of any shops here that charge, but its not "free" to the dealer, unless of course you believe time is worth nothing.
^^This. It does cost the dealer something so you, as the consumer, are paying for it. Directly or indirectly.
Only shop that I have had actually charge me for running that NICS test in Ohio is Aim Surplus. Their main business isn't walk up gun sales and you have to make an appointment, but their prices are so good it doesn't matter to me.