If polyurethane was better than rubber as a tyre compound the world would have switched to using that years ago. It's all down to the conditions of use.
(Bear in mind that my experience of the tyre industry is completely unrelated to the technical side (I was in Dunlop's computer operations area, but did have acquaintances in Tyre Technical who would have known more than you could possibly need about rubber compounds), but that was 30 years ago.)
Polyurethane replaced rubber in lots of places: printing press rollers, casters, and small wheels, cutting mats, and so on. It's suitable for those purposes because the amount of flexing is small (and in the case of a printing press the rollers are cooled by the ink and process fluids). It's not suitable for vehicle (pneumatic) tyres because of the continual (and substantial) flexing that takes place in everyday usage. Dunlop's test fleet ran a variety of vehicles under standard road conditions (with regular stops to check tyre temperatures, etc.) to make sure the compounds used were up to the job. If polyurethane was usable they'd have jumped at it with much rejoicing because it would have saved them a fortune in imported rubber and equivalent substitutes.
Solid tyres are a similar case: the rubber is being continually flexed where it's under load (i.e. in contact with the floor or inner face of the track), and that continual flexing raises the temperature of the tyre. PU gets used for things like factory forklift truck wheels because they're usually working indoors, on a smooth surface, and at low speeds. Outdoor forklifts, I think, use rubber tyres, with different tread patterns for added grip but they are still a low speed device. (Unless you talk to my friend who repairs the things after various lunatics have damaged them.)
Tracked vehicle road wheels are a high-speed, probably high-loading, and certainly high-flexing application: the ground force of the track may be quite small (because it's a rigid plate), but that's transferred to a much smaller contact surface on the road wheel, and I doubt that polyurethane is up to the task.
Chris.
(Fort Dunlop is long gone, but it used to be the biggest tyre factory in Europe, and the rifle club had a mix of members from all over the factory and admin, including a few from Tyre Technical (who were the compound and tread pattern development side of things, there were some amusing tales told).)