Wow, no one had put the actual reason for the livery being what it is.
Basically TSGN is a management contact, as a result get a fixed fee for completing certain targets, ie PPM, station standards etc.
Where as in a normal franchise you'd have money to invest from the you keep, in a management contact you have to for rebranding out of your own pockets. What's happened with GTR is they decided to keep the basic livery designed by the DfT for Thameslink and it to GN new stock too. They've kept the Southern it will cost millions to replace for no benefit to anyone at all. GatEx is being kept in line with current branding too.
The next franchise is expected to put the units into a different livery however.
That said, some bidders for TSGN were going to have a rebranding of some parts of the franchise.