Because it's a natural monopoly, they cannot be expected to break even, and therefore deserve taxpayer subsidies?

A utility monopoly is different than a profit-seeking one. If Amtrak became exclusively profit-seeking, it might raise prices dramatically cut unprofitable routes (say, to poorer towns), etc. Those things might increase profits but undermine the economic benefit that was being provided.

I expect that if they did raise prices dramatically, they would lose buisness to roads. This suggests that they are not, in fact, a monopoly.