Chariot wheels are not built like wagon wheels, they're built more like bicycle wheels -- a large number of spokes on a very lightly built wheel. In fact, it's fairly certain that wheels like this were used on Roman and Etruscan chariots at some point.

Compare this 2nd century A.D. carving to the 6th century B.C. Etruscan Monetleone chariot found in a town in Central Italy and now on display in the New York Metropolitan Museum of Art. This is a real chariot that was probably actually used, and it has a nine-spoked wheel, like in the carving you posted. You are correct that nine-spoked chariot wheels seem to be an mostly found on the Italian Peninsula; Greek and Levantine chariots of the 1st millenium B.C. usually had four to six spokes on their wheels.

It's also worth pointing out that by the 2nd century A.D., chariots had been obsolete as a military technology for more than three hundred years, and were only used in ceremonies and sports.