I've considered camping as a chasing money-saver, but in practice it is not all that practical. Many nights after a chase you're lucky to get to a hotel by 2AM to get a few short hours of sleep before you have to leave in the morning. Not really enough time to set up/take down your campsite, and honestly you won't want to deal with all of that after a long day on the road.
Sleeping in the car is a lot easier and accomplishes the same thing. Although, in some ways I guess you could call that camping too. IMO a car is more comfortable than a tent, and a lot easier to set up/take down for sleeping.
As David mentioned, you're going to have to have a pretty comprehensive list of campsites you can go to at all the different places you might end up at on the Plains. Some state park campsites are free, but a lot of the designated sites and chains like KOA charge $10-20 or more per site. With the KOAs and some of the designated ones, you get your shower in the morning with that which is nice. But, if you sleep in the car (which could be another thread topic itself) you only need to pay $7 for a truck stop shower, saving you 10 or 20 bucks on the night. If I'm spending 20 bucks for a campsite I might as well pay 10-15 bucks more and get a cheap motel. Well worth it for the degree of quality sleep bought.
The other factor is weather. From sleeping in my vehicle on chase trips often, I can tell you out there, you see what the weather is like at night - unlike you do when you're in a cozy hotel. Often it is very windy, hot, bug/mosquito infested and/or noisy (crickets). A car at least keeps the bugs out and cuts down on the exposure to the elements.
I guess it depends on the motive. If you're an outdoorsey type that likes to camp for the fun of it, that's one thing. But if the camping thought is due to money-saving measures, then car-lodging is a better alternative.
Better yet, round up a few chase partners to help split the cost of a hotel room. With sleeping bags and cots you can fit a lot of chasers in a room, everyone gets a shower and continental breakfast. All for the same cost per person as you camping alone.