Neophyte question about AC vs. DC (especially for powering a home)
It's not impossible, it's just more complicated and expensive.  Everything in your house is designed to run from AC.  Many smaller products do take DC in but they come with an AC adapter because that's the only available source of continuous, inexpensive power nearly everywhere.  The voltage required can be different for each device.  The closest thing to a standard for DC power is probably USB 5.0V, which only offers enough current for small gadgets and not anything larger.

The way a solar powered house works is roughly: solar panel to battery charger to battery, to DC-AC inverter to wall outlets, plus another power regulator &amp; meter if feeding extra energy back to the grid, which isn't a requirement.  One could power a house directly with unregulated DC from the battery if the appliances were designed to run from it, but most aren't.  If the battery voltage had to be regulated before distribution to the house, all you'd really be doing is swapping the DC-AC inverter for a DC-DC regulator, basically a different box with similar cost.

Due to the small size of the market for DC appliances (at the moment), they'd be harder to find and possibly more expensive than AC units.  If a time comes when nearly every house has solar on the roof, they might be just as easy to purchase and maintain.

As to reusing wiring, a wire is just a strip of copper and doesn't care whether you put AC or DC on it, IF you stay within its capabilities.  If you had to put a lot more current through the wire due to lower voltage, you might need thicker wires, different safety features in the wiring boxes, higher rated fuses and so on.  You'd want different plugs on the outlets so nobody made a mistake of plugging an AC device into an outlet providing DC.

Overall, it's cheaper and simpler to put a DC-AC inverter at the battery than it is to gut the entire electrical system of the house and rebuild it, plus buying all new appliances, plus still needing small DC-AC inverter in each room for the devices which can't be repurchased to run from DC - which at the moment is nearly every gadget. You might think of the AC inverter as providing "backward compatibility" with the previous hundred years of electrical devices.