The Northeast has a density comparable to Europe. I do agree on the culture issue, however - Americans definitely prefer cars by default. Although in the Washington-Philadelphia-NYC-Boston corridor it may be possible, if there is ever a culture of large public works again.
In the Northeast, Amtrak has pretty much captured the NYC <-> DC market for business travel.
What's holding it back is a lack of capacity and slower speeds than you'd find in, say, Europe.
Why it's slow is a complex problem with many causes.
It's partly due to US regulations that cause trains to be heavier, slower and more expensive than overseas.
The infrastructure is also old, dating back to the 1800s in some cases, causing bottlenecks in key areas. One 1870s-era tunnel in Baltimore brings speeds down to 30mph for what feels like an eternity.
Amtrak is also not super great at running the NEC. The physical infrastructure could do more, and relatively cheap changes could have a large impact.