I disagree that it provides any freedom at all, since you are limited by roads. If certain roads are cut off by sabotage or other means, you lose your imaginary "freedom of movement".
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.
Every freedom has limitations. Just because there are limitations doesn't mean that the underlying principle doesn't exist. People have the freedom to move, even before the car, and well before the interstate highway system.
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.
Although I do agree that cars provide some freedom of transportation, they are still heavily regulated, are more difficult to fix yourself than ever before (good luck fixing the electronics in your new BMW in the middle of nowhere), and you have to register them, buy insurance, etc. just so you could drive a extremely limited set of public roads that could be closed down any minute for a variety of reasons. Or you could just get stuck in traffic, enjoying that sweet freedom of sitting in a metal can whilst those peasants drive past you on their bicycles or other, not-as-free, means of transportation.
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.
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.