I worked for many years at a vets office, and we had a strict cage/leash policy. I'd guess that I've personally experienced about a hundred instances of someone walking in with a cat, bird or rabbit without a cage or leash because 'they are very calm and well trained', but these animals freaked out and got loose in the office, in some instances severely stressing out the animal, and also coming dangerously close to leashed dogs. When an animal is panicked they can be very difficult to restrain - trust me, my job for many years was to restrain animals (including birds) for veterinary treatments.
Just because the chickens are small does not mean they are easy to control. Most people do not take their chickens around them to the bank, park etc., so when they are taken out of their normal environment it is extremely stressful. The stress to the animal is not worth it. I once took my mellowist chicken with me to the secure yard of a residence to visit a (leashed) dog in foster care we were thinking of adopting t to test his reaction to the chicken. It was a big mistake, my chicken was totally freaked out even though the dog was calm, and I felt horrible.
We handle our chickens a lot and they are very used to us. But even occasional trips to the vet in a secure cage is very stressful to them. They would absolutely be panicked in a
Petco environment.
Our chickens are very used to our 2 dogs, but when we have friends come to our house with their dogs, our chickens stay securely in their run and they are terrified of dogs they don't know. Multiply that stress by 10 or more if you take them to
Petco.
It is unwise to expect everyone to be responsible with their dogs. I have seen idiots walk in with unleashed dogs. I have seen responsible people and fairly well behaved dogs pull their head out of their collar to get at food/prey/other distraction. I have seen this in the vets office many times as well. If your chicken freaks out and gets within 6 feet of a "competent person holding a 6' leash attached to a dog" then YOU are at fault, not the dog, chicken, or dog owner.
If your chicken goes on errands with you regularly and is not stressed by it, then by all means, PUT THEM IN A CAGE and take them to
Petco. Or at least a very secure leash and keep them in your arms. Anything else is cruel or at a minimum very risky in my opinion.