Another perspective on this is why should we expect someone else to bear the consequences of our failing to meet our responsibilities? If we're late picking up our kid, they staff at the day care leave late to see their own families, they incur higher operational costs, etc.
Their request that we show up prior to their closing time is completely reasonable and that there are stern consequences for failing to meet our responsibilities doesn't seem unreasonable either... especially in light of the comment I was responding to.... I assure you the day care really doesn't want to collect that fee.