> Which brings up an interesting question: How do you structure something with a large piece of infrastructure like a rail network in a way that could benefit from the market forces of competition and innovation?

A rail network is near to a natural monopoly. You can build overlapping rail networks, but it's complex and interconnecting instead of overlapping would usually offer better transportation outcomes and there's a lot less gauge diversity so interconnection is more likely than overlap.

All that to say, you can't really get market forces on the rails. Rails compete with other modes of transit, but roads and oceans and rivers and air aren't driven by market forces either.

Transit by rail does compete in the market for transit across modes. You can have multiple transportation companies running on the same rails, and have some market forces, but capacity constraints make it difficult to have significant competition.

> capacity constraints make it difficult to have significant competition

Thirty years ago, you would be correct. In the modern day, you could tie switch signalling to real-time auctions and let private rail's command centers decide how much to bid and thus whether or not they win the slot for putting their cars onto the shared rails. The public rail owner likely needs to set rules allowing passenger rail to pay a premium to secure slots in advance (say, a week) so that a timetable can be guaranteed to passengers during peak rush hour, but off-peak slots can and should be auctioned to naturally handle the difference between off-peak passenger rail and not-time-sensitive, more-cost-averse freight rail.