I have ridden commuter rail, aubways, and busses in New York, Boston, San Francisco, Amsterdam, London, Vienna and other places.

While you have a point that "lo-density" is an oversimplification, only New York has the kind of density and frequency of service that make public transit really usable. Boston commuter rail sucks pretty bad, with a too-sparse schedule. BART from SFO to the city is OK but around town there are too few lines and stops. This all could be fixed, but the fact is they suck compared to cities like Amsterdam where cycling has the infrastructure and the critical mass to be safe (unlike London, for example).