I do it quite often.
For International trips, I often stay at the gateway/connection city overnight versus risking a mis-connect. Airport hotel rates are usually a lot higher than if you travel a few miles out, but beyond the "airport shuttle" area. A car rental + cheaper hotel can be a lower price than the airport hotel. Plus I have the flexibility to go exploring or find a better place to eat than the hotel. A minor bonus is a few extra FF miles for the car.