>Their weapons were largely made of wood and sharpened stone

And the Assyrians largely used metal weapons.

>They had no practical applications for the wheel.

[The Assyrians did](https://arkeonews.net/chariots-in-neo-assyrian-army/#:~:text=Chariots%20were%20the%20most%20significant,(888%2D884%20BC).

>but only the Maya and Olmec had a Bronze Age

The Stone Age/Bronze Age/Iron Age paradigm is based on a specific European historical process that is very different from what happened in many other parts of the world. Pretty much none of the Americas fits this model. Many societies - the Muisca, Aztec, Mixtec, and others - had complex and advanced metallurgical traditions even as they generally didn't use those technologies for utilitarian purposes. Others, like the Purepecha and Inka, made use of metal weapons and tools in certain contexts while still using stone and wood in others, often again while dedicating the most complex metallurgical processes to religious and ostentatious creations.

The three-age system often breaks down in many parts of Africa and Southeast Asia, too. If you're interested in reading more about contemporary archaeologists' critiques of this system, I'm happy to share some articles.

There's no denying that Indigenous American societies such as those of the Maya, Zapotec, Chimor, and others were highly complex. So were those of the ancient Middle East. But they weren't as generally similar as I think is being argued on the basis of them both not fitting the Iron Age or characteristics of 16th century Western Europe.