I believe that many animal rescues self-perpetuate their own problem. Some rescues have VERY picky requirements - like salary minimums, yard size minimums, prior experience, age minimums, required seminars, required volunteer work, etc. Meanwhile you can just go to a breeder or a store, and be able to get a pet that day.
I understand wanting to make sure the animals go to a home equipped to care for the animal, but if it's so hard to get a rescuee pet that it drives people to stores, then those shelters will only ever become more crowded. A parrot rescue near me requires 6 months of volunteering for 3 hours every week before you can adopt... and there's a store nearby that just breeds and sells parrots. Which one would most people pick?