Incorporating the Thameslink operation into a regionalised Great British Railways is going to be a challenge however it is done. Given the emphasis on the devolution agenda I'd be surprised if handing some services over to TfL was not on the agenda.
As a user of both Thameslink and the Mildmay Line one of the advantages of TfL would be stations, both staffing and facilities. In particular I have more confidence in TfL on rolling out step free access.
I would also expect TfL to push harder for some of the peak hour Thameslink services to run all day such as Welwyn-Sevenoaks and West Hampstead-Orpington.
But it makes no sense for TfL to take over all of the current Thameslink operation. A good starting point is the split between 8 car and 12 car trains: as a rule of thumb the routes using 8 car trains might make sense for TfL but the routes using 12 car trains do not.
There is zero chance of different operators running through the core.
There is also zero chance of a Labour Government, having gone through the pain of reorganising the railway to bring the operators under DfT contracts ‘in house’, to then hive some of it off to an organisation that contracts them out to the private sector.