Solar for the home

Disclaimer: I am no expert in Solar power generation, nor am I an Electrical Engineer. So what I am about to request/propose might be the most absurdest thing - but for me, ignorance is bliss, and I shall propose. The biggest problem that I see about solar power is that it is available only during the day and that is not the time we consume most of the power at home (work-places is a different issue - I am addressing only homes here). We need a lot more power at night to light up our homes, drive our fans and ACs, and our televisions, and routers and what not. And for doing this, we need to store this energy in batteries. A premise that I make here is that a lot of us have inverters and they have batteries in them. But with this inverter arrangement, while we keep our batteries fully charged, we use them only if we lose power. Else it is lying unused (dormant).

Decouple the battery from the inverter.
Split wiring at home into low load and high load.
For those who are using an inverter, this would have already been done by now. Keep the high load circuit on direct power (from the utility company).
Charge the battery during the day using solar panels.
Once the battery is fully charged, divert solar power to the low load circuit to run any day time uses such as fans, TVs etc.
For night time power in the low load circuit, use the power stored in the battery. If the battery goes below a certain threshold, switch to main line from utility power company. If there is still power in the battery, even after day breaks the next day, continue using power from battery, switch to utility company only after battery discharges

Couple of advantages that I see here:

We use the power that we generate in the day time first, and then, only if needed switch to main line power in the night. So there is definitely a big component of night time power consumption that is offset. If load is low, we can perhaps offset some day time power consumption too.
A battery that is charged and discharged continuously lasts longer.

While a lot of this is based on my imagination, I am pretty sure this is doable in the realm of current age electrical circuitry. My question: Has someone done this already? Any commercial solutions?