The Portsmouth-Southampton local services should stay with Electric units, either SWR or Southern. They stop so regularly you want to the acceleration. GWR taking over the line in isolation would probably incur lots of depot overheads. Better is to let SWR operate Southampton-Portsmouth all stations locals with Southern running connections to Brighton. GWR stopping short at Southampton is probably a reasonable compromise.
The North Downs Line is a diesel island in otherwise electrified territory, and it makes sense for GWR with a large diesel operation to keep that line as they're based at one end.
You are arguing that the choice of TOC on a route should be decided if the route is diesel / electric, right? So because Portsmouth - Southampton is 3rd rail electrified it should stay with Southern / SWR, and North Downs is diesel-hauled so it should stay with GWR?!
Using the same argument the Waterloo - Exeter, and Salisbury - Southampton service should be given to GWR as well to make SWR fully electrified!
There were proposals a few years ago for a separate operator for Devon and Cornwall services, but it would have been organised with the London services also passing to that operator. Operationally, politically and financially, it just didn't make sense to split them off from the rest of GWR.
I think a better choice will be a separate operator for all non-London-mainline services in the South West, including Devon & Cornwall services, Dorset & Somerset services, etc. i.e. Wessex Trains.
I've never understood why almost every TOC name has a compass point or similar in it. I think that more generic names, especially for complex areas would be better. Virgin Trains, Avanti (without the West Coast suffix), Horizon Trains and C2C all strike me as better.
Using geographic names make the name instantly recognisable no matter which company operates the franchise. Under the newest instructions TOCs are no longer allowed to have their brand names in their trading name, for example, First Great Western has become Great Western Railway, Arriva CrossCountry has become simply CrossCountry, etc.
As long as the words "South West" remain, it doesn't matter which company operates the franchise at all and passengers won't be confused like the past when Virgin Trains became Avanti West Coast. It would be confusing if one holding a "Virgin Trains Only" ticket when the company became Avanti West Coast, but not when South West Trains became South Western Railway.