I could see this working at an airport like RNO (but I don't think the three airport hotels charge parking). You get the keys and contract inside and go outside to pick up the car. The return area is isolated from the pick up area and Avis/Budget has zero staffing in the pick up area (they put a kiosk there a few years ago which is NEVER staffed). RNO has no "exit gate" - you just drive right out.

Not all airports even have an exit gate...

Hard to see this working at a larger airport. They also need the spaces to cycle cars through for those picking up a car after you get there. You could request to leave the car there overnight then pick it up early Sunday morning before they open (can I leave the car here and pick it up early Sunday morning like say 4 AM), then just get there a little late. I doubt anything would happen.