It is not just size but a huge concentrated population
Population density is really not a big part of the equation at all. If it were a requirement, then the Lynchburg would be a total failure. The population of Lynchburg, VA is just over 60K. The same for the next few stops that train makes on the way to DC. It's not until you're in the suburbs of DC, where VRE operates and better serves commuters, that one approaches any decent population density.
The anti-rail crowd loves to trot out that population density argument as to why it works in Europe and not here in the US. But it's simply not true. Not saying that density doesn't help things some, but it is simply not a major factor either in the success or failure of a train.
Listing the population of the city of Lynchburg understates the actual transportation market. Typical with older cities, the population of the municipality is not representative of the population of the metropolitan area. The population of the Lynchburg metropolitan area is 254,000. The population of the Charlottesville metropolitan area is 203,000. Those are pretty significant markets for travel to the major NEC destinations
The statement that population density is not a major factor in the success of passenger rail is simply not supported by transportation engineering principles. That does not mean that rail cannot be viable in low density situations, but population density is a very important parameter driving the success of passenger rail. Like the "anti-rail crowd" thinks rail is never the answer, sometime the "pro-rail crowd" thinks rail is always the answer. The truth lies somewhere in between.