Having hosted at a NFS campground and travelled to a number of verry popular NPS campgrounds over the years, I can tell you what I've seen. All of them have last minute vacancies. In some cases, people leave early for one reason or another, in some cases they just never show up, in still others, they call or message online at the last minute. If you show up in the morning and are willing to wait you can often get one of those sites. But no guarantees. If you want to be sure, you need to reserve when possible. And for popular campgrounds, if they have first-come sites, you want to move in mid week. Show up friday afternoon and you have no chance whatsoever.
