Don't quite follow your reasoning.There is a differential in price already.See Scott Byrom's latest article on the forum page.
It doesn't force prices down because there is amazingly too much apathy and inertia to change.The Providers know this and (this is where I agree with you) ,they complicitly rely on a high degree of retention and all move broadly in the same direction hiking prices way beyond their input costs.It is not in their interests for any one of the only 'big six ' to disturb this arrangement.
Also there is so much vertical integration in the market they can control the whole supply chain winning from start to finish from generation through to supply.The mainly foreign owners have reaped in huge profits.
If only the regulators would get a grip on this but they have been useless for years.If competion truly worked companies like BG and Npower ,who have consistently been the most expensive suppliers, would have long lost all their customers both on price and customer service.Yes there was a drift from BG but not enough to force them to act any differently.Their cynical manouvering of the price of BG's Click 4 is a case in point.