I'm not following your logic. Having nearly triple the population density in Rheinland makes trains way _more_ feasible, not _less_. That means on average you have a train 1/3 the distance away from you. That's a big difference.

I live in NYC which has 29,000/sqkm in Manhattan and 11,300/sqkm overall. Public transportation is great here and you don't need a car.

but at 240/sqkm, that's really not much public trans per person!