Not 1% of car hobbyists wear out the tires on our collector cars. Model A Ford touring clubs are the exception probably. While there are statements all over about old tires being unsafe, it is very very rare that one ever fails. HOWEVER they CAN. Even though they LOOK GREAT, the rubber continuously deteriorates and actually shrinks. It certainly gets HARD.
Collector car tires ought to be replaced after they are ten years old simply for your driving enjoyment and less abuse to the suspension. Safety is also a reason. A Model A collector lost control of his car in my city 9 days ago WHEN A TIRE FAILED. Both he and the car are gone now.