Behind the meter storage is a fundamentally different beast, because it has the potential to drastically reduce T&D costs, which are the vast majority of bills (at least mine under PG&E).
Christopher Clack has some great economic modeling of the grid at a very fine level, showing that deploying a bunch of storage and solar at the grid edge right now will greatly reduce costs and enable far more utility scale installs in the future, because the local storage and solar reduces the need for T&D peaks.
This sort of cost optimization is not incentivized but anyone in the current setup, and is impossible to achieve without direct regulation to change incentives for utilities.
In both cases, the fundamental mistake is to think of these as costs, when they are investments with rapid paybacks and so the obvious answer (and the reality) is massive expansion of battery manufacturing capacity.
The thing to do now, is increase our battery capacity.
In California, where this applies, the grid is very clean, so yes the dirties/most polluting part of the system is probably the cars.