I volunteered for a large, breed-specific, dog rescue as a volunteer for several years. We required home visits and charged for the dogs. Shelters would call the rescue and alert them to dogs that looked like our breed, and we would always take them. Puppy millers called too, and the deal was take them or they die, basically.
We required references and home visits because people lie to get a dog. When we required a fenced yard (always for mill dogs or dog-aggressive dogs), sometimes the yard would be partially fenced and, for example, large gaps would be filled with cardboard boxes. This is not adequate.
Home visits - sometimes the homes would not be suitable for a dog. Hoarders come to mind. Sometimes the home would have other pets in it we were not told about. You don't adopt out a dog to a home that has cats when they are cat aggressive. Sometimes the owners would have children under age 6 whom we were not told about. Our rescue would not adopt out a dog to people who had children under 6, because our dogs were very active and could knock over or hurt a young child by accident.
We also required that people come from wherever they lived to personally pick up the dog, so the rescue's owner could meet them and talk to them. By this stage, everyone had been thoroughly vetted. It was a national rescue, so people came from all over the US. The dogs were not allowed to fly home in planes.
The shelter was a non-profit organization, audited by the IRS every year with no problems. The expenses were very high, especially the vet bills, which often included surgery and or teeth cleaning. Every dog went to the vet to be checked out and brought up to date on vaccines. We had many dogs who were not our breed because the owner attracted strays, or a shelter thought they were our breed, but they weren't, or because we took in dogs that were breed mixed with ours.
So many times the owner would be driving down the road, see a stray, open her car door, and it would hop in. It was pretty amazing. The rescue would try to find the owner, but rarely did. Those dogs need fattening up and vet car, and had been abandoned.
The owner took in a blind dog the shelter was going to put down. It wasn't our breed. She also took in a dog destined for the meat market in Thailand, who wasn't our breed. She adopted both of them herself, and the dogs have thrived.
Not all rescues are alike, and the vast majority have solid reasons for their requirements.