Interstate highways are designed for a speed limit of <100MPH and have the curves to show for it.

High speed rail goes well beyond that speed and needs much larger curves, at which point you're deviating enough from main roads you may as well just take a different path entirely.

Your not wrong, but not really right either. Interstate highways do allow tighter curves and do have them. However most of the interstate is straight or a gentle curve. Thus you can limit your land takings to near the curves and then rejoin the interstate. There is a good chance that the highway department will be interested in your new right of way to make the curve better too - a lot of interstates have curves that are too tight for highway use without slowing down. Many of the tight curves are also near places where you would want to slow down for a station anyway.

The above isn't a perfect answer to all situations, but it helps a lot.

Maybe in very flat areas where the interstate was preceded by nothing, but curves to avoid things in urban areas or for geographical reasons are more common. And HSR curves are gigantic; the Chinese build their HSR lines with curve radii of 4km. Texas uses a maximum of 1.4km curve radii and they have some of the fastest Interstates around.

The rail solution to that would probably be a tunnel. A tunnel is a cheaper affair with just two tracks than if it has to be wide enough for two tracks and six to eight highway lanes.

Urban areas are just a small minority of where the tracks need to go, as such if the train goes half the speed in the urban area we are still okay on overall trip time. In fact I suspect (read I don't know because it hasn't really been tried) that HSR should probably do a bunch of stops in the urban areas anyway so it won't get up to speed.

When I say "urban area" I mean the continuous built up urban area into the suburbs. American sprawl means that metropolitan areas are much further spread out than their European or Asian counterparts, to the point where most of Boston-Washington is sprawl and very little of it is farmlands.

In any case when you start building HSR it becomes progressively harder to eke out savings and the highest come from urban area speedups. Going from 50 to 100MPH cuts a lot more time than going from 150MPH to 200MPH. And the former simply doesn't work in the median of a highway.

The interstate highway along that stretch (I-15) does not seem to have enough space in the middle for that, unfortunately.