There's no reason why train operators should also own the fixed infrastructure. Truck companies don't own the interstate highway system, and airlines don't own all the airports.
Why not have private train operators (passenger & freight) bid for routes / slots / capacity on a publicly-owned rail network? Lucrative routes between major cities will return significant profits, while regional routes will require support/subsidy. But in either case, competition between operators promotes cost efficiency, innovation, and a focus on service quality.