You COULD do this. If you appliances were built to use DC. Which they aren't. Since houses are wired for AC, the appliance manufacturers design and build to use AC. That's the main thing holding you back.
There are standards in different parts of the world for what AC power should look like (120 Volts @ 60 Hz for US, 220 Volts @ 50 Hz for Europe, as examples) and light bulbs, vacuum cleaners, TVs, computers, etc. are manufactured to those standards. So far as I know, there is no internationally-recognized standard for DC. Ergo, good luck finding appliances which will use DC power distribution. There are a few which use 12 Volts DC, meant to be used in vehicles and boats, but they're pretty limited.
I've long thought it would be ideal to wire a house for 500 Volts DC and have point-of-use inverters which could produce whatever you want. 500 Volts would allow you to supply any of your existing loads with the same wiring (wire cross-section limits the amps; higher voltage = lower amps for a given load so the wires could handle AT LEAST as much as before). 500 VDC is also the maximum specification for electric vehicle quick-charging that I'm aware of.
If you were supplying 500 VDC through the house, a PWM circuit, an IGBT and an H-bridge would be enough to invert it into any AC voltage < 353 Volts. If we create AC at the point-of-use, for one plugin, not for the whole house, the components for that could be much smaller-scale and cheaper. Yes, you'd be putting one or two of these in each socket, which would drive up the total cost. But it would be possible to plug in that made-for-the-USA stereo next to the made-for-Europe lamp (or vice versa). Or, a variation on that device in the socket could supply the DC your laptop, flat-screen TV, etc. needs, directly, without converting DC -> AC -> back to DC again with the power brick. Arguably, converting high-voltage DC to low-voltage DC would be more efficient than that process. And "efficient" is the name of the game when you're running off photovoltaic panels or a battery backup.
Some years ago, I was reading an article by someone who dual-wired their house for the usual 120 VAC @ 60 Hz (USA) and 48 VDC. He was off-grid, routinely adding more loads and was trying to avoid spending money for a new, higher-capacity inverter, more batteries and more solar panels. He selected 48 VDC because he could get simple, resistor-based step-down converters for other DC devices. His answering machine ran off stepped-down DC, instead of a "wall wart" plugged into AC. Ditto for his laptop. His motion-detecting security lights used both; the motion detector was wired to stepped-down DC (yes, he had to crack the case and modify it himself) and the lighting used AC. Switching various things to DC was efficient enough that his existing battery pack lasted significantly longer and he was able to stay with his existing inverter and solar array. The resulting system, while more complex, was more efficient. This sounds like the sort of thing you're asking about.
Houses use AC because it was easier to make step-up/down transformers for AC back when all this infrastructure started to be built. At least one person has referenced the War of the Currents. Westinghouse and Tesla (proponents of AC) won over Edison (proponent of DC) because the ease of AC voltage step-up/down made it efficient and comparatively cheap to build a few power plants and distribute high-voltage power all over creation, then step it down to usable levels closer to point-of-use. DC required that the power be produced very locally, as stepping it up/down was difficult. Back then, stepping DC up meant you had a low-voltage motor turning a high-voltage generator. They didn't have semiconductor-based, solid-state switching in those days.