Wheeled carts are not very practical without draught animals to pull them. And the one place they had animals like that, in South America, llamas and the civilizations that utilized them lived in the mountains where wheeled carts aren’t practical either.
Yeah, that is a common theory, but wheel-barrows are extremely useful and have been even utilized for long distance travel: https://www.lowtechmagazine.com/2011/12/the-chinese-wheelbarrow.html
I don’t know that you could necessarily develop the wheelbarrow without first having the concept of the wheeled cart.