Look, trips like this CAN be done, but whether they SHOULD be done is another question.
When I was 17 years old, my parents and I took our tent camper 6,341 miles (I just mapped the rout) in 17 days. We also had three drivers (mom, dad, and me), and could take turns sleeping in the back of the van while the others drove, so we were able to drive through the night when we needed to.
I wouldn't do what you are proposing, but I will say this: that trip I just mentioned with my parents the summer before my senior year of high school is one of the best travel memories I have, and I have traveled to 49 states (camped in 48, but not Hawaii) and 22 foreign countries.
This is also one of the reasons I like living in the Midwest. We can hop in the car and drive east or west and see a lot of the country within a short amount of time. Someone who lives in MA or NH couldn't even consider what you are proposing.
Good luck and safe travels!