How close cars are to each other is generally determined by traffic volume. If there are twice as many cars, they can only be half as far apart because otherwise they can't physically fit on the same length of road. If you try to leave more space than that, other cars will merge into the empty space. The only way to actually do it overall is to reduce the traffic volume (or add more lanes), which is not something an individual driver has any control over.

Which is to say, in practice cars will be following too closely whenever there is high traffic volume, and systems that don't work under real life conditions are broken.