Why did no one in the New World invent the wheel?

When Europeans first encountered Native Americans, they had no wheeled vehicles, either in North America or South America. Why no carts/wagons/wheelbarrows etc? This question was addressed at The Straight Dope 25 years ago -

For that matter, the ancient Americans also had to struggle along without the true arch, the cart, the plow, the potter's wheel, the bellows, glass, iron, and stringed instruments...

The fact is that most civilizations in the Old World didn't invent the wheel either--instead, they borrowed it from some other culture. The wheel appears to have been first used in Sumer in the Middle East around 3500 BC, whence it spread across Europe, Asia, and North Africa. It didn't arrive in Britain until 500 BC. This orderly diffusion pattern makes it conceivable that all the wheels in use today are directly descended from the invention of a single gifted individual...

The principle of rotary motion... was well known... The Incas, for instance, are thought to have used wooden rollers to haul the giant stones they used to build their cities. Unfortunately, the New World suffered from a conspicuous scarcity of draft animals...

[the one New World exception] The wheel evidently was familiar to the ancient Mexicans, the only known instance of its having been invented independently of the Sumerian version. Unfortunately, it apparently never occurred to anyone at the time that wheels had any practical application, and their use was confined to little clay gadgets that are thought to be either toys or cult objects.

There is a discussion thread on this subject at Reddit today.

Photo: Kainai travois