The amount of ozone in even one hundred highly-inflated tires is nothing compared to steady exposure of continuously-replenished smoggy air.

As I said, the ozone concentration is quickly lost to any organic material that the air is contained in, leaving simply too low of a (concentration X duration) to have any significant effect.

Once an ozone molecule reacts with whatever it attaches to, it becomes neutralized. So it takes a continuous re-supply to go on to do any significant amount of damage.

Ozone, being a polar molecule, readily attracts to the differing molecular presentations of many kinds of surfaces. As such, a steady stream of polluted air (especially as when riding, or transporting a bike on a car's exterior) will cause the greatest number of ozone molecules to find homes on surfaces that present their own polarities.
Such pairing will cause significant cracking "rot" of butyl and other types of rubber if surfaces are left exposed long enough.

Gum hoods on stored bikes in bad-air areas should be kept at least loosely wrapped as I've noticed that even paper offers significant shielding from ozone's polar molecules.
The air under the paper obviously ends up seeing a lower average concentration of ozone, from either the paper's or the hood's tendency to attract the polar molecules. The rate of attack is thus slowed.