It's a great idea and even if the individual schemes came up with a version for each, that'd be a start (I may have suggested this to senior people in BRC in the past...)
GFSI doing it though... As raised above, they've not settled on one united standard for all of them but it's not a bad idea.
There is a massive opportunity from this though. The amount of time wasted in food businesses by replicating data into different questionnaires and specification portals is a waste of blooming time. It is a genuine non value add task.
In the UK, the BRC (not BRCGS) are genuinely best placed to say "let's come up with one system" because it will ultimately reduce waste in their supply chains, increase transparency and so reduce cost and risk. It's going to be the commercial reasoning which will drive this into existence not quality led.