In response to the proposal above:
1) I can agree to GN inners being devolved to TfL's London Overground provided the finances are stable and as Aictos says, they don't invest in something stupid when they can't afford to.
However I do not agree to Sutton loop / MML locals being devolved to TfL. I think that should stay with Thameslink for the sake of integration when this service interacts with 20 other services through the core at peak times. Makes maintenance, fares structure, operational convenience far simpler as well (such as interworking with other routes - not something that is done now I don't think, but don't rule it out not happening later particularly at the extremes of each day).
Any branded Thameslink service using 700 should remain with the Thameslink franchise.
2) Moving the King's Lynn back to London Liverpool Street would be an interesting move. Journey times are far better into King's Cross however Liverpool Street, at its best, isn't that much slower. However I believe it is a case that would need to be consulted with the public because it is an incredibly popular service and the question is more of a case of 'Do you want to be dropped at Liverpool Street or King's Cross?'. Any Liverpool Street service would need to make a stop at Tottenham Hale I would say, so that links to the Victoria line are retained.
3) Fully agree with this. Gatwick Express is a service that is effectively an unfair trap on tourists and those not in the know to pay double the price for no journey saving. Southern services from London Victoria on the same route are much cheaper and only about 3 minutes slower. They're also more frequent I believe than the Gatwick Express. It needs to be called out on and retired.
I would convert the portion between London Victoria and Gatwick Airport into Southern services and implement stops at Clapham Junction and East Croydon if there is demand for it. These effectively can act as crowd busters on already busy Southern services going further than Gatwick Airport.
Beyond Gatwick Airport, going on to Brighton, I would love to see these 2tph non-stop paths being given to 2 out of the 4 Thameslink services(ideally the Cambridge service as it will reduce journey times on a popular route) with perhaps either an additional stop added at either Three Bridges or Haywards Heath for connectivity reasons. The intermediate stations between Gatwick Airport and Brighton currently served by Thameslink which will now run fast, would be given to 2tph Southern service from London Victoria instead extended from Gatwick Airport (not the existing service).
If that wasn't clear, between Gatwick Airport and Brighton I propose:
2tph ex Cambridge calling at Gatwick Airport and Brighton, with perhaps a stop at Three Bridges
2tph ex Bedford calling at Gatwick Airport, Three Bridges, Haywards Heath, Hassocks, Preston Park and Brighton
2tph ex London Victoria (current GX service which would instead be a SN service) calling at Gatwick Airport, Three Bridges, Balcombe, Haywards Heath, Wivelsfield, Burgess Hill and Brighton
2tph ex London Victoria (current SN service) calling at Gatwick Airport, Haywards Heath, Hassocks and Brighton
4) Just no
5) Don't want everything devolved to TfL
6) Yes this is a good idea.