Some interesting ideas!
In a couple of years time, there are only a few things regarding England's railways which can be said for sure; that the Hitachi trains supplied under the IEP programme and the Thameslink trains from Siemens will remain where they presently operate are two of them. This is because they are parts of what are basically PFIs, and the long term contracts have been let which will ensure they remain where they presently operate until the contracts expire unless terminated early (which will incur costs).
Regarding everything else, Great British Railways (GBR) will have been established, and all contracts entered into by TOCs will be transferred over to GBR by means of statutory transfer schemes; GBR will then have the freedom to decide were the trains will be used, and they will enter into contracts with the private sector to man the stations, operate the services, etc (like London Overground).
But we don't know much more than that.
Will the concessions be similar to the BR sectors? Will they be geographic, like the old BR regions? Will there be a single livery or separate ones for, say, inter-city, inter-regional, suburban, local, etc? Will all staff wear a common GBR uniform? Simple answer to all of these questions is that we just don't know.
I deliberately used England in the first sentence because the situation in Scotland and Wales could be different; but I think we have to remember that one of the Shapps' objectives is to put the passenger first, and therefore the government won't want to see any existing services cut because of the adverse publicity that will produce. There may be some minor changes to service patterns - say the merging of the Nottingham - Birmingham and Birmingham - Hereford services to provide a cross-Birmingham one if it's operationally advantageous so to do and this also has the added benefit of restoring something which used to exist - as the fact that they are presently operated by separate TOCs will become irrelevant.
GBR will be able to look at services, look at trains available, and then decide where best to use them; so, say, GBR could decide that it was better to use 165s with their wide bodies on former GWR routes around Birmingham, thereby allowing some 172s to transfer to West Yorkshire so that 170s could move to regional services were their slower acceleration wouldn't be a disadvantage but their 100mph maximum speed can be used better than on a Leeds - York stopper via Harrogate. I'm not suggesting this specifically as a way forward, but as an example of what would be possible with a single controlling body (GBR) not being restricted by contracts between ROSCOs and individual TOCs
Regarding XC, I believe class 170s (or equivalents which can take advantage of SP differentials) are best suited to the Birmingham - Stansted service, but if they can be accommodated at Stansted 4-car sets would be better than 3-car ones; from my experience, the vehicle's layout with their wide doors are well suited for this service - much better than most of the other types of trains which have been suggested on this thread.
However, I do think the use of Voyagers (or Meridians) on the Cardiff - Nottingham service should be considered, but this needs to be matched with a change to the services stopping pattern between Birmingham and Nottingham; journey times between these two cities with a change at Toton and HS2 from there to Curzon Street have been suggested as being in the region of 55 minutes, and something similar by a direct train between them with a single stop and reversal at Derby should be achievable already if a 125moh capable train was to be used. Midlands Connect have an aspiration for a fifth train each hour in the Derby - Birmingham corridor, and if this could be accommodated that could take over the stops presently made by the Nottingham - Cardiff service.
For those of us old enough to remember, Andrew Adonis started the electrification of the GWR out of Paddington and in north west England to make use of class 319s made available by the procurement of new trains for Thameslink; GBR will be in a position to look at modernisation schemes in their totality, and so it may decide that it is sensible to "do an Adonis" and electrify Didcot - Oxford and move class 379s over to operate services on the line, and some 802s could then be available for XC services to permit more Voyagers to be doubled-up. A move like this could be attractive to GBR as facilities for their maintenance exist at both ends of the NE/SW route, and if concessions are let on a regional basis crews trained for operating these bi-modes and with some route knowledge (Parkway to the south west and north east from Leeds and Doncaster) would already exist.
I know it's easy to pick holes in the above, but I'm trying to get across the message that we need to get away from just thinking about the existing structure of TOCs when considering the question 'Cross country new traction'; in simple terms, anything's possible, and if its better short-term for GBR to swop TPE's 802s for XC's Voyagers with the latter being replaced by new electric trains as soon as the whole of the trans Pennine route is electrified, then so be it. And while thinking about TPE, it would be possible for a class 397 to operate a late Manchester - Birmingham with a return early working the following day if it was commercially advantageous to GBR - such a service would no longer need to be a Voyager
Finally, so far as I'm aware we don't know if GBR will be able to own its own traction and rolling stock; if that is possible, it might be possible for GBR to purchase stock like the 379s from their owners at an advantageous price if they tell them that they're not interested in leasing the sets at the present rates, and won't there also be "spare" class 350s too? But I can't see how either of these could be used as new traction on XC!