Yes, what Emily said.
IMO it's all about the people: there are rescues that are just jokes, and there are rescues that seem to hit it out of the park every time. My former Sheltie rescue is run by a woman who will not adopt to people of color; and she does all the adoptions. So, she's kind of the KKK of rescues. (She's also a big Trump supporter. All I can say is, I'm glad she booted me from the rescue when she did! She's scary!) And that's too bad, because non-white people make great dog owners and homes for Shelties, too.
The BC rescue I've worked with does a good job of sorting the dogs by activity level (companion, active, or working) and matching them with owners who want that level and have experience with it. The downside is they handle relatively few dogs, due to the time they spend on each one. Meanwhile, Natalie's seeding the state with Shelties: if you're white, you're alright, come on down and get a dog.
So when you set the bar that low, an all-breed rescue isn't necessarily a bad fit for a certain type or breed of dog, no.
I do think that pits and bully breeds benefit from having breed-specific rescues, with people who understand those breeds and can place them appropriately. There are so many pitties, and they are not just Golden Retrievers with big heads, they have requirements that some of the other breeds don't in terms of home environment, other pets in the house, etc. But that's about the only exception I would make.