This might be true for a particular city depending on population density and commute habits of the people, but after a certain population density is reached the

This might be true for a particular city depending on population density and commute habits of the people, but after a certain population density is reached the premise that transportation speed is inversely proportional to density holds true for the most part. Fixed line transport such as trains may not be directly affected by the density but there may be a bottleneck if the density is sufficient to saturate the lines. If the trains are running full - this would lead to increase in wait times and longer commute time.