Short line with Amtrak: there are a few. NE Central?

Amtrak doesn't use a line for free. Yes, national service (long-distance) trains like the Starlight don't pay a lot, but state-funded services added later (like Surfliner) and commuter trains (like ACE and, where not on their own tracks, Metrolink) pay pretty much the full cost of operation including a reasonable profit. In most cases the state and local agencies pay for track upgrades and the stations/service facilities needed for passenger service. So if a short line is viable otherwise there's no reason, if track and time are available, not to run passenger trains, other than perhaps PTC issues.

As for govt purchase of Coast line, I threw that in to tweak BOB2 - he's been bugged about that for years, because SP actually did offer it to the state for a quite reasonable price, but the governor at the time (Bob can tell the story in gory detail) didn't think trains were something the state should spend money on. IIRC from previous discussions, the price asked was really quite reasonable. There have been serious studies since then about adding service on the Coast (again, ask Bob for the details), so I wouldn't write off the idea of a sale if it were offered on reasonable terms. One would, of course, expect UP's terms today to be significantly unreasonable.