What IS a pit bull, afterall?

While volunteering, I've seen a few litters of puppies born at Animal Haven, and one thing I've learned is that for the most part they NEVER look like mother, and often never look like each other.

With mixed breeds, appearance can vary so much-- a couple months ago a brindle Pit-bull-type mother named Myra, gave birth two a litter of what looked like two yellow labs, one mix, and one brindle pit-mix like her:
(Below are Myra and one of her puppies, Ring Ding.)

I noticed that while Ring Ding wouldn't be outlawed in any city or state, her mother and one of her brothers would be- but they shared much of their DNA!

While mixed-breed dogs' DNA is highly variable, human perception is not. Studies show that shelter erroneously label many dogs as "Pit Bulls" when DNA tests often reveal they are wrong.

This dog, Cernun, was labeled a "pit bull mix" by shelter personnel, but DNA has shown him to be part Bull Mastiff and part Boxer.

With so much variety- even among litter-mates, what is the point in even trying to identify the breed in well-mixed dogs? By mis-labeling shelter dogs as pit bulls, the dogs are given even less of a chance at a happy life. Some shelters even kill pit bulls automatically. When dog bites occur, people often wrongly assume the breed of dog to be a pit bull, when in fact it could be a Presa Canario, a Dogo Argentino, a Boxer-mix, or just a mutt that looks like a pit bull.

In certain jurisdictions, Breed Specific Legislation mandates that dogs be assessed based on physical attributes, not behavioral testing. In Denver for example, whether or not a dog is a pit bull depends on an assessment based on 36 points- measuring the head size, chest, paws, etc.  If a dog is found to be a pit bull, you have 24 hours to remove it from the city.

With such high stakes, why are shelters labeling so many dogs as pit bulls, when DNA tests would prove that many have either no "Staffordshire" DNA, or DNA that comes from predominantly other breeds.

These dogs all look so different, but all were labeled Pit Bulls or American Staffordshire Terriers by New York Animal Care and Control:

If pit bulls are this genetically diverse, how can we ascribe one temperament-type to all of them?

What breeds do you think these dogs are? Post your best guesses in the comments (for reference top right is dog #1, and bottom right is dog #4)

Read more here, and here.