I'm wondering if the first tire installer, the one that put the tire with the sidewall problem, on your vehicle inspected the tire prior to installation. One of the tire stores I used in the past required their installers to do a thorough inspection of the tire before it was installed. The owner of the company said, and I quote, "I would rather throw away a bad tire than to see one fail and cause catastrophic damage to a car and injure or kill someone. My business would be a heap of trouble if that happened. Plus medical and legal fees cost more than a tire". I won't name names, but he is a big name in tires in a certain area of the country.
I have always bought the warranty, at today prices for tires. It only take one tire to be replaced and the warranty was well worth it.