How would Manchester to Leeds/Newcastle have a worse service? Or Liverpool to Leeds/Newcastle using classic compatible stock? If Leeds-London/Birmingham ran through Manchester without stopping the journey time would be comparable and there would still be plenty of paths for HS services across the North. The politics of 2010 were very different and the opposition to Meadowhall and Totten has not helped. Phase 2a should have received royal assent by easter 2019, the route from Crewe to Manchester will be straightforward while everyone will be still squabbling about the eastern branch. I think it will still go head but further revisions are certainly possible.
HS2 tracks are designed around the planned service pattern, which is then planned around how many passenger journeys there would be to London.
On a simplistic level, HS2 was originally designed as one core railway from London to just before Birmingham Interchange, and then a large number of different operational branches, designed for different sets of passengers. These were:
Birmingham and the West Midlands (Birmingham Interchange, Curzon Street)
Manchester (Manchester Airport, Piccadilly)
Staffordshire, Cheshire and Merseyside (Stafford, Crewe, Runcorn, Liverpool Lime Street)
Lancashire (Crewe, Warrington Bank Quay, Wigan North Western, Preston)
Scotland (Preston, Glasgow Central or Haymarket and Waverley)
The East Midlands and South/West Yorkshire (East Midlands Hub, Sheffield Meadowhall, Leeds New Lane)
The North East (York, Darlington, Newcastle)
Within these seven basic service branches, there might be slight tweaks with some calls dropped or sometimes an extra call added, but they're pretty self-standing. The intention is that trains run so that they are as close as possible to 100% full after leaving the final stop before the core. This means the expense of the Phase 1 core network is used as intensively as possible, keeping the business case as good as it can get. Obviously, some of these service patterns overlap each other slightly. The Newcastle trains obviously have to run along the same tracks as the Leeds ones until the junction to York. But, operationally speaking, there is basically no interaction between them. Newcastle trains would, for the most part, run straight through all the way to the core. London services had no reason to call at both York and East Midlands Hub, as trains from Newcastle would be full by Yorkshire and thus have no economic or capacity reason to stop anywhere south of there. Connections like York to East Midlands Hub were to be provided by the Birmingham services, which were to act as stoppers as they would have plenty (indeed, far too much) capacity to spare and would have little competition.
Since that original network was planned, there have been some slight variations. But, for the most part, the system will still be the same. Given the 200m limitation on classic-compatible branches, it seems likely that the Sheffield terminators will share paths with some of the Leeds or Newcastle services on the core. There may also be changes on the western side using the ability of a Crewe Hub to split and join sets. Ultimately whatever happens the notion that all trains will be full south of Birmingham Interchange still holds.
When you go to the S network design, the tracks can't match these basic service patterns so well. For instance, the Newcastle trains would now have a big dogleg via two city centres, when they're still going to be full south of York. They get slowed down for no good reason, making them less economic, without adding any new passengers. Meanwhile, the HS2 infrastructure in Manchester and Leeds has to be different as well to cope with the need to let the Newcastle services run straight through. At the moment, both cities have 230km/h limited branches which are able to slow down and become more flexible as they get into their built-up urban environments, reducing the cost and disruption of building them. If they had to be full mainlines, it would be much, much harder to weave the tracks through the city. You would probably need to build them in tunnels, but then you have to build tunnelled stations as well. The alternative is to build the mainline as a bypass around the city, and then still have a branch into the core. But, you then still have extra cost. On top of that, you also make it uneconomic to serve other places. The East Midlands and South Yorkshire are not important enough to justify the construction of much new track at all if trains to Leeds and the North East won't also share that track. You can't rely on the Cross Country route to get trains from Birmingham Interchange to Derby either, as they would be too slow and capacity benefits would be severely limited.
It's important to understand that the nature of what the North of England needs is very different to HS2. HS2 has to be better than two-and-a-half quasi-high speed lines (the WCML and ECML) which are already fairly fast and direct. Therefore, it has to be a massive bypass line with a very high top speed and few stops. What the North needs is mainlines the quality of the WCML and ECML to connect its major cities, when today it only has commuter and regional routes. Since the journeys are shorter and the destinations are closer together, the benefit of increasing speed above 230km/h is not worth the costs.