The amounts of local, stopper services that can run are severely limited by the necessity of allowing the big intercity trains to run on them- the different speeds mean that they cut the local services way back to avoid delays (it's very difficult to do an overtaking maneouvre in a train!). HS2 takes those trains off those lines, and the amount of capacity for local trains sky-rockets- indeed, one of the reasons why politicians in the Midlands and the North have been so keen to wave it through.
It's a more nuanced selling point than the politicians normally point to, but it's every bit as important as the time saved, if not more so- it enables a revolution across the network, not just on the HS2 line.
Here, this article explains it better than I can.
https://www.citymetric.com/transport/remarkable-achievement-environmental-case-building-hs2-4887