This line of argument makes it seem like there is a set amount of city centers when the amount of city centers is a result of dense populations and urbanisation. The thing you need to look at is why there was no urbanisation to the same extent. Europe was in no way unique in this regard, India, China, Mexico and the Andean societies were at a similar level in the early modern era.

Looking at urbanisation as the ultimate point of a society and development is also kind of a pitfall of traditional eurocentric history writing.