I'm no fan of car culture but I think to say it's the primary cause of living a sedentary life at home is an overstatement. I deliberately moved somewhere where I could walk to everything I needed including a fantastic central train station, I no longer even own a car, and yet... over the years my habits changed and I now spend a ton of time at home. My motivation to go out has simply declined.

There is a relevant concept in psychology called activation energy, James Clear provides a good introduction to it. Certainly in recent years screens seem to be incentivizing more stay at home behavior. People used to not own a TV, many quite intentionally, before our other screens were invented. But it is a very complicated topic.

Of course our activity levels change and in some cases go down as we age, but I'd like to submit that is a given, and that car-only infrastructure is an additional barrier on top of those natural tendencies.

It's simply much easier to walk to a coffee shop, or park, or wherever for those who have maintained their mobility (probably in part by living in a walking-centric environment) than it is to hop in a car, sit in traffic, for small things. It's less of a barrier.