The current market operate by people bidding to supply demand in the future. The market say "I want to buy power a certain amount between specific hours at a specific date" and the power operation can say "I will obligate to supply that energy at that time and date at this price". Batteries could at any time jump in and bid below that of any current bidders.

In that aspect we already have variable pricing. Individual customers usually don't see this, but I suspect the primary reason has more to do with averaging out the cost over time and not exposing individuals to the internal details of the energy market.