I realise that XC run that corridor as part of the NE - SW services, but I don't think it works that well. I would rethink the XC franchise (I am not a fan of this virtual open access operator trying to be distinctive when greater breadth and integration of services required IMHO). Bristol/West country to Birmingham could go to GW and Edinburgh - Newcastle to Birmingham could go to TPE. It's just a thought that currently that core Midlands/Yorkshire route needs a boost.
You are right that XC does not work very well. The threads on here highlighting their loss-making, overcrowding, delays etc all support that.
But they do provide important long journey connectivity that might be lost if it was split up.
Like the other train operators into London, East Midlands trains generates significant cash revenues that can be used to run some non-London services that would otherwise struggle or be loss making. The number and range of these in the EMT franchise are relatively modest (e.g. Liverpool to Norwich, Derby - Crewe, Nottingham to Lincoln, Derby to Matlock). In a perfect world, it would be good if EMT would invest in these routes with new rolling stock and upgraded infrastructure but not sure that's really happened.
If you were to transfer some services to the East Midlands franchise, the Nottingham to Cardiff route might be the most likely contender perhaps?
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Everyone on the NOT-BHM cross country service has to change at New Street now. I would still have a set of services running from the South West to the North East, but to be honest having experienced many XC services, including the ones via Reading it's not the best UK rail experience, so I do think multiple operators across its current network would be a benefit
There are some proposals for new services from the South-West to the North East to run on the new East-West railway, when it eventually opens. I imagine there are a number of franchises that this could be included in: XC, Chiltern and East Midlands to name but three.