It seems like this misses what I think is the point of a driving trip, which is to actually see the country? I'd give Denver to SF two weeks, to see some of the national parks and actually get out of the car and go on hikes.
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.
Sightseeing is unbounded. Your losing 40 hours driving at reasonable speeds from SF to NY before considering detours or extended stops.
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.
For me the reason is I was moving cross country and had a dog I didn’t want to put in the cargo of a plane.
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.