Too many people think every train has to go to the same place, even when there is a frequent service on a particular line.
Is every HS2 service going to go to Leeds, stopping at Birmingham, Toton and Meadowhall, possibly at 10-15 minute intervals? Of course not. There is capacity for a variety of workings. And these should include connections allowing some trains to run through to Bradford, others to Newcastle & Scotland, others to Halifax/Huddersfield.
A similar situation exists in Germany. While most ICE workings running north from Bavaria and Switzerland via Mannheim continue to Frankfurt, a few divert off and run to its smaller neighbour Mainz (and beyond).
I am not sure whether HS2 workings to Scotland should go via York though. Railway passengers from West Yorkshire and Greater Manchester have had to suffer the long diversion via York for well over a century due to the political machinations of a certain Mr George Hudson.
I've often wondered why nobody ever attempted to build a direct line from say Blackburn or Burnley to Darlington. It would cut maybe 40 miles off a Manchester - Newcastle journey. But of course such a line would need to cross the Yorkshire Dales via a endless series of viaducts and tunnels so was probably never viable either economically or environmentally.