It’s a false equivalence though, rails and roads (and the internet) are like arteries, you can have redundant arteries but it’s wasteful. So free market economics no longer apply.

It also leads to natural monopolies.

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.