There have been many experiments with automated driving systems that follow this logic and greatly decrease headways to tenths or hundredths of a second in order to improve safety. Today, modern CBTC railway signalling systems are able to significantly reduce headway between trains in the operation.
Numerous experiments with automated driving systems have demonstrated their effectiveness in decreasing headways to fractions of a second, thereby enhancing safety.  Modern CBTC railway signaling systems have been successful in achieving significant reductions in train spacing.