Here's an angle you may wish to consider, especially if you're contemplating traveling the back roads and small towns:
My totally unscientific, non-specific-fact-based impression of complaints about long delays for Roadside Assistance is that a very high number of such complaints are from folks who don't have a spare. I always wonder what they think can have been done differently since especially in small towns and/or certain tire sizes, it takes TIME for an operator to track down not just someone to change a tire, but an actual tire to boot.
Lacking your own spare, you're also in a "captive market" situation since your Good Sam coverage only covers the service- cost of parts including tires/wheels is completely outside their responsibility or control. You'll be charged whatever the seller wants to charge for the tire. No shopping around!