Existing routes, even those that can handle 90 mph in parts (like the NE Corridor from D.C. to NYC) can not be modified to take true HSTs because the routes were originally laid a) to connect urban centers, power stations, docks, etc., and b) to take advantage of the most level routes to avoid as far as possible lengthy tunnels beneath high ground, viaducts to bridge low ground, and rivers. As a result, there were few lines "at tangent" (the engineering term meaning straight) in Europe for more than a mile or so before they go off in curves again. There are, of course, much greater stretches in the USA, but generally where people wouldn't want to go.
By improving the roadbed and signaling, they did achieve a useful speed increase in Europe with the advent of diesel and, especially, electric traction. I traveled on the TEE (Trans European Express) in the 1970s, and they managed averages of over 65mph between cities, and in Britain the "Intercity 125" (it cruised at 125 mph in some stretches) was a big improvement. But these were only possible in routes that had originally been laid for speed in the 19th century. They tried an innovation to get a few more mph with a design called the "tilting train" in Britain; it banked over in curves to allow higher speeds, but was a flop (a wealthy train buff bought the experimental train and runs it on his estate).
The introduction of the TGV
(Train a Grand Vitesse), or High-speed Train, initially in France (which holds the world rail speed record at some lunatic speed like 300 mph) and later in other EU countries, required laying ruler-straight track that simply galloped over hills instead of snaking round them, due to the enormous power reserves in the electric locos. In the past, it was an acknowledged fact that the maximum gradient a main-line train could consstemtly run at was less than 1%. The TGVs effortlessly take on gradients of four times that and more.
In order to build the TGV lines, you need a government system like France's, which is closer to a dictatorship than a democracy [did you know that they did away with juries 200 years ago?] In effect, a government committee took a pencil and ruler and drew lines connecting major hubs like Paris, Lyon [
not Lyons, as you keep seeing in the press! Like oil "weight"
] Marseilles and Tulouse, and in a very few years the deed was done. Here it would never go beyond the initial planning stage, due to environmental wakos and endless court appeals from landowners.
And, of course, we're talking untold billions of dollars for a system that would never even come close to paying for itself. In fact, it would probably be a constant drain on the taxpayer. However, there may be hope yet. Harry Reid wrote a piece of pork into the Stimulous Bill for a high-speed line from his congressional district to Disneyland. I kid you not.