Not my way to see USA but many people do it like you're describing and seem to enjoy it.
With a little planning there are lots of campsites on your way, many low cost or free.
When you leave WA state pay close attention to what fuel pump you grab. Don't just grab the green handle and think you are good. Confirm by looking at what the pump actually pumps. In some places the green handle might not diesel or maybe gas station messed up?
Never had a problem getting fuel and I don't like to get down to 1/4 tank...I usually fill up at 1/2.
Bring along something to access internet. My ABS light kept flashing on and off when we were east of Rapid city. Dodge dealer wanted $250.00 to fix, but couldn't fix my problem that day. I got online and between 2 Cummins forums I fixed problem in about 20 min.
Safe travels.