Would their deal with NYS allow their use (the P32) for that type of service? Not sure if they have enough of them any way.
First, Metro-North is running at max capacity. I don't think they can spare a P32 for what Amtrak is looking for. Second, the phasing of the HEP between the two batches of P32's are different. Might be 480v, but it's there. Personally, I'd like to see the MNRR fleet made universal, but MNRR likes not being the standard.
As for someone asking about capacity, GCT is a TOTALLY different animal during the Central years than what it is today. For one thing, East Side Access took care of the lower loop and Madison Yard, Grand Central North tore out a few tracks, etc. MNRR has made GCT into a commuter station with pride. When I was born, off-peak service wasn't what it was today, hourly to Poughkeepsie on weekends, no Saturday and Sunday round trip through trains between GCT and Dover Plains (Wassaic), forget that Metro-North is in general running more trains overall. The beast is different, and MNRR is glad they have the station to themselves. On some station pairs, MNRR is running a FIFTEEN MINUTE headway during rush hour. Amtrak trains don't run with Shinkansen precision. That said, MNRR is cutting back a little Harlem Line service for a few months (track and station work in Westchester County), so there might be some wiggle room.
I've argued that everything except for the Lake Shore should be a through train, but we'll be lucky to get what we get. The MTA is trying to run its commuter railroads with an attitude best reserved for rapid transit. Hell, I'd like to see Amtrak operate a few trains out of GCT permanently once Penn Station Access is opened (also contingent on ESA) and some New Haven Line service is moved to Penn, but that's another can o'worms.
TL;DR: Metro-North is protective of its railroad.