This is sorta true in part (in some places) because other options like walk/bike/bus/train have been so disinvested that in many places you really do need to own a car to get around with any level of dignity.
It does seem to be changing on larger US cities though, so I’m hopeful.
I dont think Americans care for the current road monopoly states have, or the monopolistic tolls and enforcement.
The idea of freedom of movement isn't really a European-centric ideal - its more uniquely American and derived from being a nation derived from those escaping injustices of Europe and searching freedom and liberty.
With the history of Europe being based in serfdom - peasants being forced to work their lord's land for protection - the idea of freedom of movement never really seemed to be of importance.
Those who deemed it important probably emigrated from Europe to America.
Car dependent societies don't allow many choices, you are restricted to only choosing a car for transportation.
Regarding it being an "American thing", Germany was the first country to build highways, and currently the highways there (Autobahn) don't even have a speed limit, so you could say that they provide more freedom of movement than the roads in the US.
The Autobahn was constructed for a similar goal as of the Interstate highway system - to act as a transportation backbone for the military during conflict. The fact that it's grown to what it is today is because it was built with free money (for the cities and states building them) and it became one of the safest ways to travel long distances without having to spend a lot of money.
Regardless, there's a lot more freedom to a car than a politically charged public transit system tied to a social credit score or even economic ability to pay whatever arbitrary fare exists. While cars do cost money, they also tended to keep going with a lot of abuse, and aren't tied to how politicians think of you.
Are cars cool? Absolutely. Are they some kind of freedom machines? As much as oil companies and car (excuse me - freedom machine) manufacturers would say otherwise, no.