As toadbriar said, breed rescues will try and take their own breeds out of pounds, it frees up space for other dogs, and puts dogs into the hands of foster carers who understand the breed and can probably make a good job of finding the right home. Particularly with breeds which might have particular needs, this makes a lot of sense.
But there are other issues. In Australia, for example, legally, stray animals must be kept for eight days (the number of days varies a bit from state to state) in order to give the owner an opportunity to reclaim it. At the end of the that time the shelter may release the animal for sale, or euthanize it. Most of the regulations around the operation of pounds and shelters set a maximum length of time an animal may be held in kennels before it is released into foster care, killed or possibly moved to another facility.
Because of the pressure of the sheer numbers of dogs coming through pounds, most pounds can’t afford to keep dogs indefinitely, even if they were allowed to legally, there are always more dogs who need the space.
Most rescues rely on foster carers to look after dogs they take out of pounds. It is usually easier to find foster carers for small dogs than for large dogs, it’s often a question of space, the carers other dogs and confidence in handling bigger dogs. I’m one of the few people I know who has the space and the experience to take on big dogs.
Rescues also have to be realistic about the dogs they take and make hard choices about which dogs are going to be easy to rehome. Rescues rarely have a lot of money, so one dog which requires lots of rehabilitation or expensive medical care means that ten dogs might miss out on being taken into rescue.
Dogs which are easy to rehome mean that more dogs can be rescued because space opens up with foster carers. For rescuers it makes good sense to take on dogs which they know are in demand and will be easy to place. Large, mixed-breed dogs, particularly black ones, old dogs and some breeds can be very hard to find homes for and rescuers need to be realistic.
Amongst the rescue people I know, what usually happens is that they will put their names on dogs in the event that the dogs run out of time, but will hope that the dog gets adopted rather than needing to come into rescue. There are occasions when pounds will only release dogs to rescue, but that will be particular cases (very small puppies/pregnant bitches/dogs which might need extensive retraining/some breeds or temperaments).
There are good reasons for the adoption fee. In the first instance experience has shown that people value things they have to pay for more than they value things they get cheaply.
Rescue dogs have already been through the mill, nobody wants them to repeat the experience. Someone who is willing to pay $200 for a rescue dog might be expected to value that dog. It’s not always the case, but it’s a start.
A dog which has been adopted from ethical rescue will be vaccinated, desexed, wormed, deflead and had any necessary medical treatment. Sadly, some pounds still release dogs undesexed, so while you might get the dog cheaply, as a responsible owner you’ll still have to fork out for all those things.
Chances are that if you paid for all of that yourself it would cost more than the adoption fee of a rescue dog, since many vets will offer cheap desexing to rescue groups. If a dog is already desexed then what a rescue makes extra on that dog will go to defray medical expenses on another dog.
I don’t know any ethical rescues which make money, most of them spend more on each dog than is ever recovered in adoption fees.
The kinds of dogs which turn up in pounds might also reflect the population of dogs in a particular area (I’m in a rural area, we see a lot of working dogs, for example), and/or the kinds of dogs which people don’t value.