I wonder if we'll see something like [TGV speeds c. 350mph]
Nope. Never on the East Coast, and that's OK.
Density is a two-edged sword: it slows you down due to old, constrained Right-of-Way, but it also allows you to connect a whole lot of markets (passenger $) even if you're not going that fast.
David Gunn repeatedly points out that the NEC's advantage is time (city-center to city-center of some of the richest metros in the world), not speed. Japan's Shinkanen debuted at 130 to 137mph, and indeed Acela I has already taken
Amtrak's share of the combined rail-air market from DC to NYC from 37% (before Acela) to 75% (today). They kicked the airplane's butt (cut them by more than 50%), basically, and longer, faster Acela IIs are only going to make it worse for the airlines.
Given big cities close together and air service frustrated by congestion, the train can "win" without super high speeds.
We'll also see that tunneling a few miles to new stations under downtown Baltimore and Philly is a cheaper way to reduce door-to-door travel times than would be building and maintaining many many miles of new track between cities.
Eliminating a 20 minute cab ride from BAL Penn or PHL 30th Street to people's true destination at the Inner Harbor or at Center City (or easy transit connections there too) is a bigger winner than going faster in between.
Except for a possible HFD-PVD shortcut, and maybe an LIRR-to-New Haven Sound Crossing, there isn't going to be a call for long stretches of new track, and speeds will never need to get past, say, 180mph (France's TGV debuted at 170mph and that first line now runs at 190mph...and is profitable)
The new, lighter, Acela II trains will print money even if they only rarely get to 165mph (in central NJ, in RI/MA and maybe, one day, on improved lines in northeast Maryland)