It seems very sensible to get a coherent plan for HS2/HS3/NPR whatever at Manchester Piccadilly, before it seemed like the HS2 plans might conflict with HS3/NPR.
I can see a possible option where HS Manchester to Leeds might get built *instead of* rather than as well as the HS2 East Midlands/Sheffield/Leeds leg, with the East Midlands given the sop of full electrification and some further speed upgrades of the MML, and maybe Derby to Birmingham electrification and speed upgrades. As an East Midlands resident I don't *like* the idea of us being somewhat sidelined again but in the bigger picture it might make sense.
This option has been looked at to death, and still doesn't make sense even if NPR and Phase 2b are now one project. The fundamental problem is that any east-west line is going to be very different in nature to the north-south line that HS2 provides. That means running north-south trains like London-Newcastle over it would involve serious compromises. You'd end up with worse north-south and worse east-west trains and for relatively little benefit.
The basis of north-south journeys is end-to-end city/region pair routes which can largely fill up their own trains. By the time a train passes south of Birmingham Interchange it'll be full so that its path on the most expensive and congested section is the most valuable possible. Some trains will be full further north than that. A Newcastle train will probably be full after picking up passengers from Darlington and York; a Leeds train will probably fill up with the East Midlands and possible Yorkshire Parkway stations. Once a train is full, there's no value in doing anything other than sending it the direct way to its destination. That's how the via-Manchester idea falls down: a Newcastle train will already be full, so it shouldn't stop in Manchester or Leeds as it'll just slow down Newcastle/NE passengers while not providing any more seats for people from Manchester or Leeds. Building an east-west line that doesn't slow the Newcastle passengers down would mean big sweeping curves (presumably in tunnel) under both the cities and a station or station bypass capable of high speed running. These are really not what would make it easier to do east-west journeys.
For east-west journeys there aren't as many city pairs that can reliably fill entire trains on their own, and that's entirely fine. Frequency, reliability and capacity are more important than headline city pair journey speeds for most east-west journeys. A 6tph express service from Liverpool to Leeds, stopping in Manchester, would be a hell of a lot more useful for most people than one which can maybe go a few minutes faster by not calling at Manchester while being a lot less frequent in return.
The actual trains themselves should probably be quite different for north-south and east-west services. North-south needs 200m sets designed to double up for the stretch to London which can run at 360km/h or so to make the most of the high speed non-stop running capabilities of HS2. A future Scotland-London train should, once there is a dedicated line all the way, be able to run non-stop at 330km/h+ all the way from the Glasgow/Edinburgh junction in Lanarkshire all the way to the Ruislip tunnels on approach to OOC. East-west trains won't ever spend as long cruising at high speeds since average journey lengths are far shorter. The longest possible stretch of higher-speed running would be on the existing ECML from Darlington to York! That means a top speed of 230km/h or so should be more than sufficient. The trains themselves also probably need to be 200m at maximum, and would benefit far more from being universally classic-compatible so that they can easily run off any new lines into existing stations and further-flung points on the network. The difference would essentially be the same as on HS1 between the long-distance Eurostar services and the shorter-distance Javelins. It's possible the NPR Javelin-style trains might be specced up to slightly higher speeds - maybe 249km/h to keep below the TSI compatibility threshold - so that they have an easier time being pathed alongside north-south services on any longer stretches of HS2.
