It can also bring graft, fraud, and a raft of other abuses, as well as rapacious, extortionate pricing of necessities.
The relevance for Amtrak is this: You need not look further than the government contract with the private business that's been building new Viewliners to see that "involvement of the private sector" is no panacea, and that "the private sector" can't simply be relied upon to be "imaginative, innovative," or even competent.
And, in the bigger picture: If all aspects of Amtrak are to be "improved" by contracting them out to profit-seeking businesses, then what happens to the parts that don't turn a profit? Any NATIONAL passenger rail network will have functions that are not profitable. Why shouldn't the government run the whole thing, allowing the profitable aspects to subsidize (at least to some extent) the unprofitable public services--rather than enabling businesses to cherry pick the profits leaving taxpayers with all the debits?