DC is much less workable at low voltages like 12v or 5v common in household application -- the P=IV equation is more dominated by current, so with more current the resistive losses add up quickly even in a run across your house (it'll be down to 10 or 8v by the time the wire reaches the far end of your house). Not to say some people haven't suggested wiring homes with 12v lines... data centers have implemented (or at least experimented with) DC distribution due to the density of DC devices.
Also there's always capacitance which will cause some loss for AC but of course capacitance won't affect a DC transmission line. HVDC also makes combining different electrical grids extremely simple as there's no phase difference or frequency difference to worry about. DC also requires lower peak voltages as AC is going to be sqrt(2) times higher than the rms voltage.
DC power lines are also better underground or undersea, they don't suffer from the capacitance to the surrounding material.
The AC-DC conversion equipment at each end has a cost, but for 300 mile aerial lines or 30 mile underground lines it is currently cheaper to do DC.
There still might not be enough power loss to matter, but even with 70-80% efficiency you're still talking an extra 25-50% batteries over the ideal.
If you are using it to power a very light load, the efficiency will be much worse, as it takes a minimum amount of energy to run the inverter.