There is also the liability aspect where shelters always have that possibility of being sued if an adopted dog injures someone
I don't know as it's even that - shelter workers as a rule know what awesome dogs pit bulls are - but where I worked we did not spay/neuter, and we also did no
home checks. Anyone with $45 could waltz out with a dog.
You can imagine what kinds of people would be adopting the pit bulls, especially an unaltered one, with no background checks, and only $45??
To me, it made more sense to send them to rescues who do
alter, and perform home checks plus assess the pit bull to find out what type home it should have (cats, no cats, dogs, no other dogs, etc.) and make sure it's going to a responsible, pit bull experienced home, than it did to just shove them out the door to whomever has the adoption fee.
That's not even to mention how many places have banned the breed, maybe not necessarily in that town (in our town they are/were) but perhaps surrounding areas, or perhaps fear that someone won't check with their homeowner's insurance and find themselves in trouble due to that. To top all that off, even if legal in the town, many renters find themselves homeless or having to bring the dog back to the shelter when they are told their landlord won't accept the breed.
Anyway, there's many reasons shelters don't adopt out pit bulls to the public but I'm guessing the reasons are more complex than liability.
Because if it was just liability, no dogs would be adopted out, period.