They do - but as the rate you are paid for electricity is now a fraction of the price you are charged, most people without a battery try and align their energy use with production.
( The suns out! Put on the washing machine/dish washer etc ).
Sure - don't know what proportion of solar panel installations that is though - it was an early adopter incentive.
Bottom line - not all the local solar production is measured at the grid level - much of it results in demand reduction which can't be directly attributed.
I think this will only increase - either due to local batteries, or more electricity driven heating systems ( heat pumps for example ).
And this isn't just homes - if you have a farm and have a big water reservoir which you fill by pumping water - and you had some solar panels - you'd just run the pumps when it was sunny - there is no particular need to run them at particular times ( same if you had a wind driven pump ).
( The suns out! Put on the washing machine/dish washer etc ).