My younger daughter used to go out with her friends and they asked one of the parents to drop them off, then they all shared a taxi to the nearest home, slept on the floor and asked to be picked up next day. I was happy not to have to turn out at around midnight as I sometimes did for my older daughter.
But I made sure both knew that I could be called at any time if neccesary rather than e.g. getting a lift with someone who wasn't fit to drive.
I'm more or less teetotal so this was no problem, I suppose your solution might be to say that you would pay an emergency taxi.
But they need to have some consideration, so you are right to ask for it as well as giving it. (If you don't teach them, who will?)