The issue is that they can't just close when they want if there's a child still there. So they have to have some way of enforcing these rules on parents. A "per minute" fine seems appropriate, so that it's more the later you are. And you need the fine to be enough that it is punitive enough, when considered against the income of your parents. Otherwise it provides no incentive. Ours is not $300 (more like $30), but it seems fair.
And then there's the challenge of keeping people on staff at all when parents consistently make the staff work late.
Beyond that, it seems like a good way to achieve the objective of convincing parents to not offload externalities onto others by being late.
I'm shocked by your question. I honestly would like to hear why you think this should not be acceptable. Why should they continue working overtime and cut into their own personal/family time because of the parent's failure?
Let's say you have a job interview. You're 5min late, so they either don't hire you, or the receptionist says the interviewer is now not available. Are you now due the salary, because you being this late 5min cost you a lot of money?
If you in a private contract reject the terms of paying $5 per minute late, well then the other party now knows you plan to be late a lot, so they'll be glad if you take your business elsewhere.
Keeping people from being able to go home after their workday, effectively forced overtime, is incredibly disrespectful. And even if "it's not your fault", you are the only one that could have prevented it. So incentives should be in place that you don't. $5 per minute sounds fair.
If you force me to stay late for a full hour you'd BETTER pay me triple digits. But in this case the $300 for an hour may have to be shared among several people.
The point is to encourage people to NOT make use of the service.
I can't understand how one can treat people like servants, forcing them into unpaid overtime, to wait until I'm good and ready to show up. And to be upset and call it "unacceptable" to compensate people when you mistreat them.