I think it's great to try to connect people with animals they want to take care of. It's not going to make overcrowded shelters any less crowded. There is certainly some unused shelter capacity that your organization can fill up, that is true. However, that capacity is not infinite, and once you have reached it you'll have all the same problems.
There is only one solution: subsidized spay/neuter programs and a crackdown on any animal-breeding operation. Otherwise, you're just giving a blood transfusion to a patient with a gushing wound.