By the way, Amtrak does not use all of its right-of-way. There's room for 6 tracks in the Bronx, but it has been reduced to 2 tracks. What do you do with the space for 4 more tracks? Work things out, and the subway will come really cheap—possibly cheaper than light rail. Of course, not every place has extra space just to plop a subway on top of. The Bronx just so happens to have this.
Anyway, the reason subways are claimed to be cheaper in the long run is not the immediate monetary cost, but the effect on the surrounding ecosystem. By building lower capacity transportation, you physically cap the growth of a region to a certain level. Imagine replacing even a single East River tunnel between Queens and Manhattan today with a light rail or BRT line. The ridership was definitely not there when some of these lines were built, but had the city or companies operating the transportation went for cheaper options, Queens would not have grown so much. Stunted growth is a residual, ongoing cost that will make the community pay for a long time. That's why compromising on transportation is such a bad idea.