Check your Touring Tires?

I've never been very happy that mine came with Firestone tires. After purchase I noticed which model, FR710. This vehicle supposedly went through a total redesign maybe a year earlier. Did they design it around a 10 year old tire was my thought.
Just past breakin, 500 miles, I traveled about 130 miles on I-95 and became quite unhappy with handling. Major point is play in steering, still unresolved, but feel a better tire would help overall with handling, ride, and noise. I've voiced that opinion to dealer as well. I've even checked on some new tires, but also had nagging feeling that I've finally figured out.
My window sticker, just below the wheels on vehicle, clearly states "touring tires". Firestone FR710 are NOT "Touring Tires".

I've checked the Firestone/Bridgestone website and other sellers of this tire and it shows up as "passenger tire, all-season". It is definitely not listed as a touring tire of any type.
I also learned that in the size needed there are few touring tires available.
One of the few available unless you wish to go to a much higher speed rating is the Michelin Primacy MXV4, grand touring all season.

Did GM think no one would notice that the tires they installed did not meet the window sticker?
I suspect GM owes many of us a new set of tires.