Maps showed about 1 day and 18 hrs so I accounted for 3 day rental but lodging slipped my mind. So probably another $200-$400, if leaning towards economy options.
5 days * 8h/d * ~73 MPH will take you from SF to NYC, which only needs 4 hotels on the way. However, if you’re including stops in that 8h or fail to avoid traffic it can take a lot longer.
If you're spending all day driving, might as well fly?
Though, there are other reasons to do it, like if you're moving stuff along with your car.
As such 5 days is just a reasonable baseline. It lets you see the country along the way, have some slack, and show up without being exhausted. Got an extra day, week, or month and you can find plenty of things to do along the way, but you still need to account for the underlying distance. Alternatively, if you’re in a hurry there’s plenty of ways to cut that down.
Most of the times I've driven across the US, I was either moving, or transporting a vehicle.