I don't about the 'dump the customer' just because they express what they want. It's more a case of can you increase your profits by giving the customer what they want. It's worth a try.
If the job is worth keeping then say to them that they call you when they want you but it will cost more, at least 50% more, because your prices reflect how you organise your business and a call out affects your profits.
It's not that the customer is then running your business and not you. The trick is to arrange things so as you still make money from them and preferably more money than previously.
If it becomes hassle or causes you problems, then dump them but I'd try other approaches first.
As for customers who are out. We have a pre printed letter and envelope with a first class stamp on it. It looks proffesional.
Last year out of nearly 5 000 SAE's, only 63 didn't send a cheque. Of those 18 said they'd sent it, but still paid, 40 had forgotten and 5 ex customers never paid.
When we used a just a slip with our comapny name and address plus the amount, there was constant non payment problems with far less customers.