I generally endorse this kind of reasoning but you should keep in mind that this doesn't work in part because a lot (probably most) don't generally endorse it too.

In the case of the daycare, the price wasn't intended to encourage parents being late at all. The actual price the daycare workers would probably want to charge is not a market clearing price, but a price so high the market doesn't clear. They probably felt trapped into haggling once they put any price on the practice at all.