Humane societies, unlike the other types of shelters (and I can only speak for my own geographical area) Usually want to give the prospective applicant time to think about the committment they are about to make. The 24 hour waiting period is to cull out the impulse buys (so to speak). There are a lot of people who will take home the cute kitty without REALLY thinking about it, you know, as a lifelong committment. So 24 hours gives them time to think about it and back out if they are not truely ready for cat ownership. Also, if you can't be a little inconvienienced by a trip to pick up your new family member, how serious can you be (and I do not mean YOU, Mary, I just mean people in general)
I also find that the humane sociaties (again, vs. the other types of shelters) are not committed to DOING the neutering themselves. They require it, and most likely insist on a refundable deposit until supplied with proof of it, but it's the OTHER shelters who tend to JUST DO IT !!! I guess it's a money issue.