Well, I admire the motivation, as it was similar to mine, but a battery merely timeshifts solar. If you don’t have a battery, your excess solar is exported to the grid, which has the effect of making the grid cleaner since it displaces fossil generation.
So all the battery is doing is changing who gets to use your excess solar. Is it primarily you (battery), or is it your neighbours (no battery)? In environmental terms, who uses the excess solar is irrelevant. It is therefore your solar panels that are creating the environmental benefit, not the battery.
Yes and no.
So, I export power to the grid which makes it available to my neighbour. The thing is they get zero benefit from that because they will still be paying the exact same rate their power company will charge them at that time of day. I'm benefiting no-one by exporting at that time of day.
Exporting excess solar to the grid is not necessarily a good thing and it isn't going to displace fossil fuel based generation in any real way.
Basically, if I didn't have a battery, I'd be exporting any solar I'm generating but not consuming. This will be replicated across every house with solar (and no battery). This means that in the middle of the day where domestic solar generation is high but domestic consumption is low, there is an excess of power on the grid. We have already seen the effects of this with lower and lower FITs. In some jurisdictions the FIT drops to zero at peak production times and some even get charged for exporting to the grid. This is becoming quite the problem.
Now, later in the day domestic solar production will drop but household consumption will increase (people coming home from work, cooking dinner, etc.) and there will be a great need for power. It is these peak period where fossil fuel based generation gets used the most. If they are gas powered stations there is some flexibility to increase production to meet demand but with coal based production there is little scope so those plants run 24x7.
You nailed it when you said that a battery time shifts solar. This is exactly the point, except you make it sound like a bad thing when in fact it is a good thing.
If I store the solar I'm not using, I'm providing two main benefits:
1) I'm not putting power into the grid at a time it is not needed
2) I can use that stored power from my battery instead of the grid, lowering the demand on the grid when the demand is at its highest (at least from a domestic perspective).
At some times of the year, I'm not using any power* from the grid from a net perspective. That's less power that needs to be generated. At other times of the year I may need to pull some power from the grid but I am able to do this when the demand is low and it is power that would go to waste anyway. So, overall, I'm using less power from the grid at any particular time, and what power I do take from the grid, I'm taking when there is low demand.
What I'm doing in my house alone is not going to make much difference, but could you imagine if every house had solar and batteries? That's where we should be heading. It is not the only solution, but it would make a huge difference and would reduce the reliance on fossil fuel based generation for domestic use.
Perhaps a better solution would be community based storage but I can't see that happening with the current infrastructure.
* I still have a HWS on controlled load grid power but that is pulling power from the grid when demand is low and when it dies I'll replace it with a heat pump and power it from the powerwall.