Let's say a client decided to end the service with a hosting provider and he/she really doesn't have the time to go through the whole process officially through a billing ticket request. If a client would just stop paying for service with numerous reminders that he/she receives by the system anyway, it likely means the client is no longer interested in the service and doesn't want to get charged anymore. So if you go ahead and charge the client a late fee, what would that accomplish except now angry client?
I understand that not letting the company know about you no longer needing the service is a little lazy and a little douche-y, but that probably happens more commonly.
Most companies just have it outlined in terms that they would terminate the account if the client doesn't pay for 30-45 days. It then becomes client's fear that he may lose access to files if he doesn't do something. Charging an account reinstating fee (or access to files fee), in that case, makes it a lot more fair.