Funny discussion this. A lot of generalizations that, generally speaking
, are not allways true.
Whether older sets of rubber tires work depends, as some have already indicated, a lot on your setup as well as how you treat (additive, cleaner etc.) your tires. You can, and some regularly do, win major events on old tires. For example in the 2001 Euros one of the Dutch drivers tried new tires and did not like them. The reason was that he usually runs practice heats on old tires, so his car is setup for that. He decided instead to use a set that had about 10 runs on them already. How he did? He qualified 6th and still on the same set of tires he finished 6th too...
Ok, a dated example. So a more recent one. In the Netherlands our national championship is contested over a series of 6 events. Each consisting of three heats and 2 finals. For the whole season we get only 6 sets of tires, so basically one per event. The first national I ran one set. The second one I ran the same set and, contrary to some of the other competitors including the reigning Dutch Champ and current championship leader, decided to stick with that set. End result? TQ and a win...
Older tires don't have to be slower, assuming the car is setup well and the tires haven't become too soft. The latter is especially important when temperatures are high. Moreover, even if the tires have gotten too soft due to too much use of cleaners and/or additives (mostly motor and brake cleaners mess up the tires sooner) you can still get more good runs out of them. Simply put them away for a couple of months to dry out again and they will work well again.
So why do people run new tires at big events? Well, for one thing because you have to. Because nowadays we use control tyres that are marked at the big events you have to run a new set at least once. Outdoors the difference in handling between a 1st, 2nd and 3rd run can be pretty big (after the 3rd run things tend to settle down giving consistent handling from then on). This means you have to adjust the setup to adjust for the changing balance in the tires. Add to this changing racing conditions and you make life a lot harder for yourself in terms of finding the right setup each round. So, on major ourdoor events, if you can, it pays to run a new set each run.
For club racing getting sets that have been run only once or twice is excellent. They are still basically new and from the third run onward, if well treated, will give consistent handling and balance making it ideal for both races and testing.