I have, however, come up with an imperfect model to show that tread compression is real.
The victim is one of my model rock crawlers, chosen for its supple, compliant tires and easily-measured tread lugs.
The large and small lugs are .255 inches apart when the tread is uncompressed. Forgive the use of Imperial units.
I don't have a piece of glass large enough to support me on my bike, so this will have to do. You can see how the tread flattens out under the load of gravity.
The moment of truth. The caliper, set at .255, will not fit between the impressions made by the lugs. This was not a rolling impression but a static one. Best measurement comes in at .245, for a compression of .010 on a 5-inch OD tire.
The model is imperfect for the following reasons:
1: the contact-patch/diameter ratio is wildly exaggerated.
2: measurement the impression is somewhat imprecise, due to the nature of the impression (dirt on ATM envelope).
3: the tire itself has no fabric reinforcement; it is pure synthetic rubber. Fine for its intended purpose, but unsuitable for a bicycle.
4: the tire is not pneumatic, but supported by foam inside the tire, for technical reasons we won't go into here.
Nevertheless, the model shows that tire treads do, in fact, compress when flattened out. Take this for what it is worth.