That one time my overnight bus broke down at 3 AM outside Rock Springs, Wyoming. I spent six hours in a gas station parking lot trying to sleep upright while a radiator hose got fixed. The thirty bucks for a roadside motel room the next night felt like the best money I ever spent. You save cash, but you're trading a real bed and a quiet shower for a coin flip on whether you'll actually arrive rested.
Man, I feel this. I tried the "tough it out" thing once on a red-eye. Got to the station at 5 AM with my neck completely locked up from sleeping on a bag. Had to just sit in a diner for three hours until anything opened, totally wrecked. That cheap bed is never a waste when you're that worn out. You just can't put a price on actually being able to function the next day.