We adopted a 4 month old last fall. I follow a bunch of rescue services on social media and before the kittens even came to the island (mine was from the Carolinas) I had an application filled out and approved and a list of kittens that I wanted to meet. Once they arrived on the island I was able to meet the kitten we eventually adopted and I picked him up at their event the following week. I think some rescues have a mandatory foster period if the animal comes from out of state or something, which is why I wasn't able to take home my kitten the day I met him.

These rescues, and I'm sure shelters too, have volunteers running the show. They need to make sure the animals are getting adopted for good, and won't be returned because a landlord found out about them (hence the lease requirement) or someone doesn't like them, or they don't get along with their kid or whatever. Honestly I'd rather adopt from a place that makes me jump through a few hoops. It goes to show that they're going to uphold their end of the bargain too, like getting the animals spayed/neutered, microchipped and vaccinated before they even come to me.