Because the land is cheap, it is generally easier to expand and drive, and also because the US auto industry is 3 million jobs directly, 13 million indirectly, 2nd biggest auto industry on the planet, and so politically I guess it would cause problems to push for biking cities.

"The population density in thousands of places in the US is more than high enough to support more sustainable transportation solutions, but yet even those places don't."

Places where the population density is high enough to have it (New York, other parts of BosWash, Chicagoland) by and large do have it.

The OP was complaining about Los Angeles. Five minutes with Wikipedia and a calculator will demonstrate why mass transit sucks there, and always will. And LA is dense compared to most of the country.