I fully agree that you should always check with the Campground host or other manager, even if all the sites look to be full/reserved. I have had several situations where that has helped me land a campsite.
However, I'm curious which NFS campsites you've seen with no charge reservations? I can't say that I've ever encountered that. If anything, my frustration with campsite reservations is that campsite reservation fees often cost nearly as much as a single night of camping. Most NFS campsites tend to work through Recreation.gov, the last time I used it not only charged a $10 reservation fee, but required prepayment of the site. The not only was the reservation fee not refundable, any cancellation would involve another $10 service fee.