I believe the "flat spot" tire issue is an old wives' tale.

That used to be true in the days of bias ply tires, but not so with modern radial compounds. Hence our forfathers would store vehicles with the tires removed and the chassis up on cement blocks. Some folks still do the same today.

Other than environment and age deteriorating the outer treadwalls (as others have pointed out), you should be okay. but if you are unable to get them to hold air, the tires may have lost their bead against the rims.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car