I take your point since if you imagine all TPE etc services transfer to “HS3” that would in theory free up a lot of space on Castlefield and at Victoria.
That said, it’s highly unlikely the TPE services on existing lines would be taken away, since politically that’s very difficult to do. They basically become standard “semi-fast” services, with the centre-centre traffic transferring to HS3.
It’s here where it begins to make sense to try and get the best value out of one piece of future infrastructure as possible. With HS3, you still need such a cross-city tunnel to relieve Castlefield (not to mention the increased demand to feed Piccadilly). You’re more than likely going to need an underground station at Piccadilly to actually run NPR trains onto HS2 reliably. That station will need to be 450m in length to fit HS2 trains, with 6 platforms so HS2 trains can terminate. (Alternatively a turnback under the city centre) Both options are extremely costly and have been balked at by both the DfT and treasury. (Not that there’s any change there!)
So if instead, you start by upgrading chat moss (partial 4-tracking) and connecting it to TRU & Piccadilly via a relatively short tunnel, you can run both long-distance intercity and semi-fast (TPE/EMR) services through it. You’d get 10-12tph.
Then Castlefield and the tracks through Victoria can be ran exclusively by TfGM metro-style or “S-Bahn” services.
We need to start looking three steps ahead and seeing the bigger picture.