Has anyone ever been able to make a reservation on that site? Anytime I look at locations they’re either closed, or booked, or you have to plan a half year in advance.
The popular sites are booked within minutes of opening up. [Thus the complaints about bots.] That said, many of these sites have a limited number of spots reserved for walk-ins. So, have a couple of back up options if you're going to try your luck at a popular site.
Sites that don't have electric or water hookups may be easier to get since they're less popular with RVs. And the folks with RVs are experts at campsite reservation.
That said, go off the beaten path. Less people make for a more enjoyable experience. Some of my best car camping experiences have been on the side of a forest service road, especially one accessible only with a high clearance 4x4.
Sites that are accessible only by foot, even a half a mile in, are usually not that crowded. But you'd have to backpack in everything you'd need for the stay.