The reason to discount it is that paying up front is otherwise more expensive than paying in instalments. By discounting it you're factoring in the time value of money and it would then actually cost the same. I agree with you that they're doing it as a service to people but the notion of discounting as if that provides the customer with a benefit is misleading.
It's like buying your phone outright up front or buying on a plan, the upfront cost is always going to be less than paying in instalments.
Regardless, if people really hate the idea of paying instalments, put the money in a bank account and pretend that's them paying to the club, then let the club take the instalments out of there. Basically Dennis' half-joking suggestion but really it's the same thing..