I don't particularly see a point in rebranding everything. Most rail operators are representative of the area/region they primarily serve anyway (LNER, Cross Country, West Midlands Trains, Greater Anglia etc etc.) and I think that regional brand identity is important.
To maintain that under a single brand you'd almost need GBR Northwest Regional, GBR Northwest Intercity, GBR East Midlands Regional... it quickly gets quite messy and that would all overlap anyway.
When I think of say Liverpool Street, Greater Anglia almost instantly springs to mind. When I think of West Coast I instantly think Euston, and so on. I think that brand differentiation has become ingrained in a lot of people's travel.
Not to mention it's a monumentous task to complete that wouldn't come cheap. Changing the external liveries is one thing, but you'd need to standardise the interior look and feel, audio/ announcements and visual screen guidance to name a few to really do it justice. You then have a whole host of rolling stock with very different characteristics largely associated to the train operator as it is currently, so you're never going to get a truly consistent product across all regional, or all Intercity services.
For me, GBR is nothing more than a kind of internal, government branding for the nationalisation of the franchise operators, rather than something that should be directly a customer facing brand to define all British rail.