I would make the argument that the supposed "cost savings" of owning a car are based on the structural requirement to own one based on American city design, along with hidden subsidies by the taxpayer.
Roads are not just funded by usage taxes like gas taxes and tolls, but also by general tax revenue.
"Aside from gas taxes and individuals’ expenditures for their own driving, U.S. households bear on average an additional burden of more than $1,100 per year in taxes and other costs imposed by driving." [1]
That means, if I don't drive, I'm still paying for the roads and other periphery costs as a taxpayer.
The second argument I'd make against cars enabling lower costs is the city planning argument. North America has basically ignored mid-density development in favor of a downtown core + sprawl formula, so if you don't want to own a car or if you want to drive your car less frequently you're limited to a very small portion of the housing market that mostly exists in high cost areas.
Building ordinances and zoning laws also contribute to this problem, with parking minimums for homes and businesses making car ownership a guarantee (i.e., if the parking lot is so huge that it's impossible to walk across you're going to drive).
Tokyo, for example, maintains a completely flat housing cost over time due to housing policies that encourage housing supply [2], and the Tokyo metropolitan area has much lower car ownership per family than the USA.
Finally, it's important to point out that the USA enjoys low gas prices through its currency being the main currency for oil transactions, its own massive quantity of domestic oil production, and rather influential foreign policy. Cars are cheap in the USA because it has the ability to make that choice, but at the same time that choice is relatively unnecessary and wasteful considering how the US is overwhelmingly urban and suburban (i.e., it has enough population density in the places most people live to support a less car-focused development pattern. Sure, people in rural areas need cars, but people in Secaucus, New Jersey need/have cars due to conscious city planning choices).
[1][PDF] https://uspirg.org/sites/pirg/files/reports/Who%20Pays%20for...
Disclosure: USPIRG is generally biased against highway expansion according to Wikipedia.
[2] https://www.wsj.com/articles/what-housing-crisis-in-japan-ho...