Seems like you're just asking if an RVer can travel around these days with no plans/reservations. We used to do that years ago when we had a small Class C without tow car. RVing has gotten more popular with both intentional RVers and those without sticks&bricks homes. But I think you can still do it...IF...you aren't picky about where you camp (first or second choice may not be available), if you stop earlier rather than later in the day, if you don't go near popular tourist sites, and if it is not a holiday. That said, you might still run into full campgrounds because an RV club happened to book most of the campground for the day(s) you want to stay (happened to us), or people are escaping a wildfire, etc.
There are many websites that list many different kinds of campgrounds...private, city, county, State, Federal...but I have not seen one that specifically lists FCFS campground/sites. No one website is totally comprehensive. I have a whole list of websites saved that I use....here are a few:
https://freecampsites.net/
https://uscampgrounds.info/
https://campgrounds.rvlife.com/
https://www.rvparky.com/
You can also search BLM, COE, USFS, etc.
Now our camping style has changed, due to age and disability. But sometimes, if we are just driving a long way to get someplace (with reservations), I just book each night in the morning before I leave the current campground.
Best of luck!