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You’re cherry picking statistics. Or maybe you just don’t know history. Los Angeles, your prime example, was developed mostly around trolleys, and only later became car dependent. In the 1920s it had the world’s largest trolley network. There are admittedly a few cities that make this claim, but at the very least LA was among the great transit cities on Earth a century ago.
In fact, there was a time when every US city (even smallish ones) had an extensive trolley network. We purposefully ripped most of them out in a concerted effort to decentralize our cities, which worked exactly as planned.
And EVEN THEN there are far too many US examples of new transit-oriented communities to peg the difference on history. Places like Arlington, Virginia and Portland, Oregon. And of course, the presence of New York, Chicago, and San Francisco obviously destroys any argument about the US as a whole being too large for urban cities (not to mention Moscow, Saint Petersburg, Toronto, and Montreal).
There is a historical difference, no doubt, but you’re giving it far more weight than it deserves. The key differences came after World War 2, when the US adopted urban renewal policies that gutted our central cities, and suburban growth policies that over-subsidized suburban growth.
The easiest way to prove this is to look at Canadian and Australian cities, which are if anything even newer than American ones, and equally wealthy, but are generally more urban, more transit-dependent, and more European. There is no explanation for this except government policy.
Density within cities does of course matter, but there is absolutely nothing about the US that means its cities should be inherently sparse. SOME of them are sparse because we intentionally made them that way, but many of them are not. There is no overarching inherent rule, no predestined form. To suggest there is denies reality.