It also falls down on its not just time slots, but the relative speeds of the services, the number and location of stops and the time taken to embark/disembark at each station dependent upon the type of train and number of passengers on that service. It's also dependent upon the number of lines e.g. 2 pairs or lines (one fast one slow), just one or bi-directional, and the signalling layout (can only ever run one train per block).
I defer to your expertise on this, but my understanding is that it wouldn't create those problems if they don't already exist. Rival companies would effectively bid to run specific services (or bundles of services) within a constrained timetable against certain obligations.
It also falls down on its not just time slots, but the relative speeds of the services, the number and location of stops and the time taken to embark/disembark at each station dependent upon the type of train and number of passengers on that service. It's also dependent upon the number of lines e.g. 2 pairs or lines (one fast one slow), just one or bi-directional, and the signalling layout (can only ever run one train per block).