For me the big advantage in buying tires from Tire Rack or Discount Tire is selection and service. I am very particular about the tires that go onto the vehicles of "me and mine." Tires are the most important safety and performance component on a vehicle. I want the best combination of wet traction, dry traction, snow traction, handling, noise, ride, treadwear, reliability and cost of ownership. Even though there are hundreds of tires that will hold air and roll down the road I want one of the few tires that will satisfy my needs and wants. I just cannot find that at a local tire shop at anything close to a fair purchase price and I will not compromise to accommodate their limited selection.
Then there is the issue of who is going to install the tires. I like to use the small shop that I've gone to for years for state inspections and tire mounting. I know them, and I know the guy who will be doing the work. I don't have to explain to them about match mounting, balancing, the placement of the tires on the vehicle, not scratching the wheels, using tire lube, cleaning the beads, etc. Everything is done right every time.
It has been my experience that the odds of getting the right tire at the right price, with all the installation details done right, the first time, drops dramatically when purchasing from the chain stores. I still call around locally when buying a set of tires and give the chains a chance, but I still wind up buying from Tire Rack or Discount Tire and having them installed by people I trust. It is by far the best deal.