Why would 3 days late on your rent involve a court date and eviction?

If I recall, the last few leases I signed had clauses like a $25 late fee for up to a week overdue. And as a landlord, at least here in NH, if somebody doesn't pay immediately, and you want to get rid of them, you have to deliver a written demand for rent, which allows X number of days for response, before you can commence eviction proceedings.