the shop said, "You're good to go, we'll bill you later."

You'd say something like, "Wait, how much do I owe you?"

Shop, "Not sure, we'll see what equipment we used, who worked on your car, what oil we used, and if any contractors came in to help and then let you know."

We just wouldn't be ok with that and we'd never use that shop again. But, for something as important as our health we go get services with zero idea of cost, when we'll be billed, and what the bill even means when we get it.