I think you may be a bit ignorant of the law here. Read 'where service animals are allowed' at [1]. The American Disabilities Act states pretty clearly that to deny reasonable accommodations to disabled people is illegal.
To create an analog to your argument. Lets say an individual is in a wheelchair and a store doesn't have ramp accessibility. In your argument, it would be perfectly fine for the individual to abandon their chair and crawl into the store because the store isn't barring that individual from entry. The issue in this analog (as with your argument) is that for the disabled person to function they need access to their wheelchair (or dog). Denying access for the dog is equivalent to denying access to wheelchairs which is equivalent to denying access to the individual.