The "commitment problem" as you state is not actually the problem. It is the practices of most fitness businesses that is the problem. Honesty for one is a term that has been lacking in this business for a over 30 years. Customer service is the other. Many owners are committed to making the sale and when it is sold that owner does nothing to keep that sale (or relationship).
If you want to solve the commitment problem than you need to begin in your own backyard. When someone gives you their money that should be the beginning of a beautiful relationship but more often than not that owner forgets the customer's name after the check has been written. I'm not saying that you need to be every customers best friend but you do need to show that you care about them.
The fitness business has always been a sales oriented industry and is finally figuring out that it is better to re-sell an existing customer than to go find other ones. You still need to keep up your marketing efforts because of attrition but when you create a community where people can come for real advice, friendship and a sense of belonging then you have solved the commitment problem.