This doesn't work well when the flat occurs in a remote location, or when it is too late to get to the local shops before closing time. And Costco declined (by phone, as we searched for service) to fix a tire on my other vehicle because we didn't buy the tires there. Of course, because is was a new car still with the factory tires.
Costco won't do anything unless the tires were bought through them. They do this for liability reasons.
Heck, if I didn't sell someone their tires, I'd be disinclined to fix their flats too. That said, there are places that will, just to pull in business.