If you have a collector car or an unreliable car, I can see how that could make financial sense. If you have anything that people would describe as a "normal, reliable car", that does not seem like a money-saving move. 1600 miles of mostly highway usage is not particular stressful on a car.

Depending on your car, it could easily be 30 cents / mile in depreciation + maintenance costs. So that's "worth" $480. Depending on how long of a trip and the type of car, the rental may well be cheaper.