All the more reason for local storage. The closer to the end user that the power is stored, the less load on the transmission lines. If you store it at your own house, it never needs to hit the grid at all.
Yes, that's a good thing. However, imagine a world in which everyone has local storage and only needs power on the 10 days of the year when it's dark and rainy. So, let's say the total power draw per household drops to 100 kW per year (about $15 at California power rates), vs perhaps 10,000 kW per year today (about $1500). Meanwhile, the cost for maintaining the infrastructure changes very little -- crews still need to come out and trim trees away from the lines, pull fried squirrels off of transformers, re-string lines after a storm, etc. Assuming half of your current bill is spent on infrastructure, the utilities would need to recoup $750 or so per year from their customers to provide that $15 in power.