I ran Amtrak trains for about 2/3 of a 32-year career. Fastest I ever went was 110 (on one of the old Turbotrains on the Hudson line). Most of the time, considerably slower.
In most of the territory I covered, the trains today don't run much faster (if at all) than they did back when I hired out in 1979.
Even Amtrak's Acela only touches 150mph for a few 10-mile stretches up in Rhode Island and Massachusetts. Too many curves otherwise.
New York to DC (not my territory) has good stretches of 125mph running.
There are stretches of the upper Hudson Line (NYC to Albany) that are good for 90mph, another modest stretch for 110.
There are some areas of Metro-North (part of the Corridor) where speeds have been LOWERED in recent years, not raised.
You're not going to see any "high-speed" rail on existing freight lines. Even where it might be possible (out west), the slower freights will be "in the way".
The only prospect for true high-speed rail would be on dedicated rights-of-way reserved for such trains. The cost of land acquisition and construction will be higher than astronomical. Look at "California high-speed rail" for an example.
Even if it was cheaper to build, you won't find many places where -- once operational -- folks would choose the service over other modes of transportation.
If you've read this far, the Acela service between Washington and New York and New York and Boston wasn't that bad. In fact, it offered a good alternative to driving or even flying if you needed to get from Boston to NYC, or from NYC to DC. Ever tried driving the New England Thruway through Connecticut at rush hour?