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.
Any individual driver can still maintain that spacing. If a car pulls in in front of my Tesla S it will simply drop back slowly until it achieves the set spacing (actually measured in time not distance) again.
There are very few roads in my experience where long stretches are filled with high speed cars. The places that are filled with cars are usually around accidents and road works where the speed and hence separation distance are reduced.
I don't think a three second separation has any meaningful impact on throughput. perhaps someone with the necessary expertise and tools could simulate it.
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.