Even with the network controlled by a "neutral" entity limited capacity means you can pretty quickly reach a situation where additional competition can't happen

Even with the network controlled by a "neutral" entity limited capacity means you can pretty quickly reach a situation where additional competition can't happen without actively worsening the schedules of the existing operators. Timetabled connections are likewise impossible to set up with too much uncoordinated competition, because without making the connection times unattractively long they cannot really be set up between more than one train per relation (maybe sometimes two at a stretch). Plus connections that aren't ridiculously padded (and therefore result in absolutely uncompetitive journey times) really only work with some sort of through-ticketing so passengers aren't left stranded if they do miss a connection after all.