Having a credit policy ensures that your organization has the cash flow to operate. If you give everyone service and are relaxed on how soon (if ever) to actually cash in on those receivables, you may have some assets on your books in A/R that will never be realized as cash. If you never get the cash, you are going to go under soon.
One thing to note is that in public service you might have to essentially give away services at some point. The book talks about hospitals doing charity care, but it can operate in the same manner in different organizations. You should have a development department to make up for the shortfall in funds from services. Having a firm, defined credit policy about who gets credit and who does not will help the planners in your organization make plans on budgets and cash flow.
In my experience, there is an interesting other side to this. Our biggest funder is the state of Illinois, with almost 70% of our operating budget coming in from them. If a funder is a big enough part of the budget, you lose leverage over your policies. Even in good times, we have to plan cash flow on not being paid for service we do right away. Service today might be paid in January. That makes our planners have to be reactive to the state’s whims.