Almost 2/3 of Americans live in states with population density comparable to Europe. The real issue is that the density is too uniform to make rail a viable form of transportation. If you take a major American city and the surrounding suburbs and drop it in Europe, it will likely cover several cities, their suburbs, and rural land between the cities.
I don't think this argument really holds up in a world where China built twenty-eight thousand miles of HSR in two decades, a lot of it connecting disparate urban areas much like what the US has:
Those lines generate insane losses just to operate and maintain them
As @jltsiren noted, this is a false equivalence. You need to compare the population densities where most people actually live, not overall density. When you do that, a very different picture emerges.