As the parent says, the solution would be to add dedicated high-speed rails, but then you loop back to the US density issues. How fast would the Acela have to be for it to justify the price you'd have to charge to ever come close to paying back the cost to add a whole dedicated train line between Boston and Washington DC?
No faster than it already is, I would think. The experience is SO much nicer than taking an airplane that a little extra time is worth it. Don't forget how much time is wasted in airplanes just getting to and from the airports and waiting for security checks and sitting on the tarmac waiting to taxi. Trains travel directly between city centers with almost no waiting time.
The Acela doesn't really need to be much faster, though it'd be nice; it just needs to be cheaper and more frequent.
This goes to what I was talking about in my initial post. Right now, part of why Amtrak is bad in the US is because we're getting pretty efficient use of the same rails for freight purposes. The ways around this would either be to somehow legally force freight to fully be lower priority than passenger, which presumably raises prices/lowers efficiency of freight on the rails or to build a mostly disjoint system of rails for passenger only.
The costs required to build a passenger only system is high and the density of the US makes me question if it would get the use needed to be viable. In the meantime then, is it net positive for the US to prioritize freight use over passenger? Even if we gave passenger traffic maximum priority, would it defer enough flights to offset the freight efficiency losses?
If you want to see the real Railways of North America, check out these interactive maps [1]