Pittsburgh is on the other side of the (eastern) continental divide--the Appalachian Mountains--from NYC. They're not the highest but they'd still cause a lot of difficulties to HSR. I also doubt you'd have enough traffic just to Pittsburgh and NYC-Chicago is too far. Even if you wave your hands and reduce the current travel time by half to about 8-10 hours, very few people will take that rather than fly.
NE Corridor already works well for train obviously. Amtrak has various plans to upgrade service though I don't know the current status of those plans.
Half that to 8–10 hours? It's only ~350 miles or so, and if we're talking HSR, by the standards of the past thirty years is only a couple of hours or so. The other thing worth remembering is that some of the steepest grades on railways in the world are found on HSR, up to 4% compared with 1.5% that would be considered steep by the standards of most railways.
Fair point about the grade (given right-of-ways for dedicated track). However, it's over 700 miles as the crow flies. It's academic in any case. This would be a project in the $10s of billions and isn't going to happen in the foreseeable future.
NE Corridor already works well for train obviously. Amtrak has various plans to upgrade service though I don't know the current status of those plans.