If you look at the average amount of space taken up by a person traveling around if they walk, or take transit, for most trips then they'll on average take significantly less space than using a car.
In the far past some trips were taken via horse + carriage but tons more were taken via walking and transit. Our built world has scaled to account for that increase in space used on trips.
But if 80% of day-to-day trips are walked and 20% are horse-carriages that's much more efficient in terms of space than a world where 80% of trips are via car and 20% are walked.
That additional space manifests in more wider roads to reduce bottlenecks and more large parking lots to store cars at different destinations.
I've phrased this multiple different ways. The concept isn't complex: a car (or horse carriage!) is much bigger than a person walking so if we design a world that encourages more travel via car (or horse carriage!) that world will be less spatially efficient.
But, as I've pointed out repeatedly, in the past far more people walked to take trips than take a horse carriage.
I feel like you are trying to say that it will require less space? Like roads can be made narrower or shorter? Why though? The road width is defined by the vehicle size and the number of lanes, and you don't want to cut the number of lanes below 1 but realistically you want 2 so a broken vehicle won't block traffic for everyone. And there are already not many 3 lanes in each direction roads so you are not saving much. Also most 3+ lanes roads I see are arterials and interstates, people driving those routes usually cannot walk them physically as they are tens if not hundreds of miles.
If every destination needs parking for nearly its peak capacity then that creates substantial sprawl.
Similarly if an area gets a high volume of peak car traffic then over time it will tend to get more arterials and interstates connected to it.
As sprawl and road networks increase it becomes more difficult to get around without a car, incentivizing more cars, which requires more large parking lots / roads.