True, but I don't see how you can have a "free market" on a train track otherwise. You've got to schedule trains, you can't have them coming and going as the market reorganises. And there's little possibility of choice, there's usually only one reasonable route to get somewhere, people don't want to add 6 hours of their journey time, to go via an alternative route.

There are competing operators in various places in Europe, the UK included.

The clearest example is probably Hamburg-Köln-Express in Germany, which operates trains that take around the same time as the state-owned incumbent (DB Fernverkehr), but on older rolling stock for a lower price.

The hard part is "how do you divide up the capacity on the infrastructure", but this is a problem that has clearly existed throughout the EU since 2007 (when there's been open access freight operators), though has in reality existed much longer (most international services, for example) hence track access and allocation being the subject of an EU directive all the way back in 1995.