There are always exceptions and edge cases. Plantations and farms are generally neither known as examples of urban design, nor are they homes for majority of population of any state.

But even using the example of 18th century plantation - the idea of a parking lot for more than a dozen or so horse drawn carriages seems somewhat... straight out of Flinstones.

I agree that You can find some early examples of the modern "carriage-based" urbanism earlier than in the 20th century, but those would be very specific cases. If 90% of the population lives in some denser urban setting and mostly walks, "their" neighborhoods will reflect that in how and where they are built (at least after a generation or two that's necessary for construction). Same reasoning applies if that ratio changes and within a generation or two, everyone suddenly can afford to own a car. The question is now which way do we (and, by proxy, the politicians we elect) want to promote.