If you are on utility battery power, will they let you charge your EV?
The other problem with grid connected battery power is the inverters and their design. Typically very high switching frequencies (like greater than 2 kHz). These can have negative interactions with other loads on the distribution circuits and cause lots of problems for large end-users. These problems are extraordinarily hard to model and predict because they are so dynamic. Ask me how I know...
The more crap we connect to our grid that is rapidly switched (power supplies, battery chargers, etc.) the more issues we will see. Residential consumers will notice shortened life of appliances, computer power supply, and UPS's within their house. Even with very clever topology the fact is these are solid state (digital) circuits supplying power from the grid connected batteries (and solar and some wind turbines). This source of power can never truly replicate analog power coming from a generator. Listen to a vinyl record and then a low sample rate digital recording for an example. The digital recording will sound like ass compared to the pure analog vinyl.