Please don't perpetuate the myth that the rescues themselves (and their rehoming rules) are the cause of there being 'so many dogs in rescue'.
The rescues are there trying hard to pick up the pieces caused by (amongst many genuine reasons) over-breeding, puppy farming, unsuitable homing, impulse buys then thrown away, lack of training, lack of even basic understanding, 'don't have the time', 'child is allergic', 'doesn't get on with other dogs', 'chases cats', 'can't be left alone', 'it cries and messes all the time (it's a flipping puppy!) and even - and yes this has happened - 'no longer goes with the decor'.
Unfortunately rescues have to do an awful lot of weeding out and thus have to set the barrier pretty low with rehoming criteria but most have some flexibility within the parameters. Look at it this way: at the point a rescue dog is accepted into a rescue it becomes their dog and hopefully a good rescue will treat it as if it were their own pet and will take every care to rehome it permanently to suitable home and family.
If breeders and dealers took as much care initially as the rescues do there would be far fewer dogs endlessly circling round the free-ads, being passed from pillar to post and deteriorating a little in health and behaviour each time, ending up in rescue if they're lucky. Or, even better, hold off on the breeding and importing of pups for which there are just not enough homes.