In most states puppy raisers would have no legal right to take their pup with them in public without first getting permission from the place they plan to visit. Remember that puppy raisers and service dog trainers are two different things, so even if the state has trainers' rights, they don't necessarily apply to puppy raisers.
Puppies need a wide range of experiences, but it really isn't necessary, or even well-advised, to take them everywhere. Outings should be carefully planned with specific goals. Outings should be well-controlled. Most agencies using puppy raisers require them to attend weekly training classes and give them very specific rules about outings.
Socialization is a term frequently misapplied to "taking a pup everywhere." Socialization is not about places at all, but about meeting and interacting with other living creatures, including as many different kinds of people and dogs as possible. Habituation is the process of getting a dog used to different places. It is not necessary for a pup to experience every store in town to learn about being in stores. What he really needs to learn are different kinds of flooring surfaces, different kinds of entrances, different smells, and different distractions. Each of these should be practiced first at home and friends' homes, then at dog school, and finally "on the road," but in very controlled situations. If a pup suddenly faces a slippery floor, aggressive dog, and noisy/grabby children all at once, he can be overwhelmed and emotionally scarred. He needs to experience each thing individually and with sufficient control that he is not overwhelmed. A young pup cannot handle as much stimulation as an older pup. So each outing needs to be customized for that particular pups personal development. At eight weeks old, screaming kids at 20 feet was about the limit of Ruby's tolerance. Ruby and Oz were my most recent puppy project. By 14 weeks, she was running in a pack with the kids. At six months, she was in an elementary school gym with several hundred kids petting her. There were many many other steps in between. The point is her exposure to kids was gradual and very carefully planned and controlled so that she would always be confident and successful in the encounter. The result is a very confident young adult.