[stordoff]

As I understand it, it's because there often aren't 'local lines' per se. For instance, if you want to go from Doncaster to Retford (about a ten-fifteen minute journey)[1], you're either on the East Coast Main Line (which runs Edinburgh-London) or the Hull line (which runs Hull-London). The necessity to runs express/intercity services on the same line reduces the ability to schedule local services - a slow moving/frequently stopping local service would block express trains.

It's less about moving local traffic off current lines, and more about freeing them up to provide local services. You could potentially see something like Bawtry station[2], which is between the two, brought back into service if there is demand, whereas it might not currently make sense to do so as the line's primary purpose is intercity travel.

[1] Not necessarily something that might be affected by HS2 - just a set of stations I know as an example.

[2] Closed in 1959, but Wikipedia notes: "land near the station has been protected should the site be required as a new station, with car parking facilities, in the future as the town grows". The line initially went Doncaster-Rossington-Bawtry-Scrooby-Ranskill-Barnby-Retford, but now only Doncaster and Retford remain.