This is so frustrating! I'm currently looking for a dog, and the shelters near me have a few special needs dogs, a few "lab mixes" or "shepherd mixes" that are obviously Staffordshire terriers that happened to get lucky by having long noses and slightly less boxy heads than the average 'mix', but they constantly have trucks of pit bulls and Chihuahuas arriving from Texas and Louisiana and Mississippi.
Pre-COVID, I went to a pet expo and met a staggering number of these breed rescue groups. There are no Goldens at any shelters, but there's a golden rescue. No Weimaraners at any shelters, but there's a weim rescue. No dalmatians, but there's a dalmatian rescue. No greyhounds, but there's a greyhound rescue. No huskies, but there's a husky rescue. There are no pit bull rescues, I'm guessing because they'd be accused of operating a fighting ring, and if they tried to snap up every dog that matched their requirements they'd be inundated with ten thousand dogs.
Those breeds don't need rescuing, they get snapped up from the shelters faster than I can hit "F5", probably because (as you said) shelter intake staff are calling the breed rescue groups before even listing the dogs.
I don't think I'm a pitbull bigot, but I'd like an actual choice in adopting a dog, and I don't want to pay someone a thousand dollars for the privilege of 'rescuing' it. It's almost enough to push someone away from the shelters to buy from a backyard breeder...