Certainly competition can drive innovation and a quest for excellence. However, for a service which is provided on a subsidized basis is the cost structure really going to be significantly different than it is under a public-run entity such as Amtrak? As Iowa Pacific has demonstrated the hard way, an improved and upgraded service will attract more passengers but implementing such innovations is hardly "cost neutral". It requires more money, and thus a greater subsidy. Assuming the status quo, the cost for private industry to provide the same level of service as Amtrak is also likely to be similar - but the private company expects a profit margin on top of the expenses.
I understand your point and agree that a private operator needsto make a profit and this will come at the cost of increased ovrall subsidies.
So if your primary objective is to reduce susbidies, government ownership and operation is the way to go.
However, in my view susbidies are not the only factor at stake. trains do not exist in a vacuum but only really make sense if they are well used and appreciated.
We have recently seen lots of stories about people like Mica micro-meddling with Amtrak's catering. For the managers and staff having to actually run the whole thing that must be extremely annoying, and must be diverting their energies from more directly pressing issues. If you are at the mercy of somebody who doesn't like trains and the whole thing might well be shut down in 6 months time, that's not a good basis on which to build confidence or growth.
A private company would sign a contract with the government. the contract would lay down the level of subsidy but also the level of service, catering, etc etc. If the company fails to meet those criteria they would pay fines or be punished in some other way. But at least people like Mica can't come and micro manage anything because there is a legal contract for the duration and you can't come in and change a contract without both sides agreeing. So if operating contracts could be awarded for a period of say 8 tzo 12 years as in the UK, you have greater stability and are assured of a flow of future subsidies taking much of the risk out of what you're doing.
So yes, it costs more, but it may be worth it.