A few things here:
Yes it's only a marginal time saving, but it's still an improvement over now.
However the big benefit, and again this is where people generally only look at their own bubble and also where HS2 has been criminally mis-sold, is the capacity that would be released by HS2.
The current fast LNER trains from London to Leeds calls at 5 or 6 stations including King's Cross and Leeds. Along the East Coast Mainline between London and Leeds, there are no less than 35 stations, the vast majority of which those fast trains pass straight through. They are served, but those services have to work around the fast intercity trains.
When you move those fast trains over to HS2, either on an Eastern branch or via Manchester, that releases a huge amount of capacity on the existing line for new and improved services.
Between Wakefield and Leeds there is just one station on the ECML at Outwood. Removing those fast trains would free up room on the existing network providing capacity to add new stations in the South of Leeds that currently wouldn't be worthwhile as there isn't the capacity in the network to call at those new stations. Alternatively if it proved better, without needing to accommodate fast intercity trains, that line could be reworked into a light rail/tram line that runs on the existing rails until the edge of Leeds city centre, then goes onto a regular tram line through the city centre.
Combining HS2 and Trans-Pennine services into a single new build high speed line between Leeds and Manchester has a far better business case than that line plus another high speed line coming into Leeds from South Yorkshire & the East Midlands.
Manchester wants that Trans-Pennine Link. Leeds wants that Trans-Pennine Link. Liverpool, Sheffield, Hull and Newcastle also all want it. Get that built first, get the fast journey times between Leeds and Manchester (and other Northern cities that would use it), release capacity on the existing network for new and improved services, and then go for the HS2 eastern branch that improves journey times to Leeds.
HS3/NPR would have used part of HS2 South of Manchester. Now Manchester has lost HS2, the cost of that section would have to be included in the cost of HS3/NPR making that scheme more expensive and worsening its business case and BCR. That has an impact on Leeds, Liverpool and the rest of the North, so no, Manchester losing HS2 is not good for Leeds.
Liverpool is "happy" Phase 2 has been cancelled as Manchester would have had a far quicker journey time to London than Liverpool would (5 mins difference now vs 20 mins difference after HS2 Phase 2). They view that as falling behind despite them actually getting a faster journey time to London than now.
Leeds is "happy" Phase 2 to Manchester has been cancelled.
Westminster sees this infighting and glee from Northern cities when another Northern city loses out. Meanwhile the whole of London and the Home Counties generally agree on infrastructure. What is good for one part of London is good for another. That is what the rest of the country needs to do as well. We need to stop comparing Leeds to Manchester and Liverpool to Manchester and start comparing the whole of the North to London.
If you want to compete, pit HS3/NPR against Crossrail 2. At the moment I'd place money on Crossrail 2 being built (or at least starting construction) before HS2 goes North of Birmingham or HS3/NPR starts.
