Low voltage distribution won't work, even just inside the home for high power devices.
Low voltage both needs a bigger wire due to higher current and at the same time is more sensitive to voltage drop (5V drop for a 12V line is much worse than 5V drop for a 220V line). So, plugging in a computer (300-500W more if it's a gaming rig with four video cards) or a big TV (150W) or AC (1kW or more) or electric kettle (2kW) or something else that uses a lot of power is not practical with 12V.
OK, so let's up the voltage to 48V. Now the TV needs 3A, a PC needs 10A and the kettle needs 42A with permissible voltage drop of 4.8V. This can be doable (except the kettle), but you still need big wires and outlets. Also, you still need DC-DC converters for most devices as they do not run on 48V internally.
As for having three different voltages (12, 48, 220 AC), that would be really inconvenient. Do you want to be able to plug in you vacuum or kettle in every room? Well, every room has to have a 220V outlet. And those are where the highest power devices will be plugged in. OK, your phone can charge on 12V. Do you want to run a separate cable just for the phone? How much power will it save? When the cost of running the wire will pay off in the conversion savings?
As for battery backing the low voltage and not backing the 220V - well, if my heat pump, AC, furnace and servers are connected to it, while my phone charger is connected to 12V, guess which line I will want to have backup power?
Also, backward compatibility. If my radio can only work on AC, then I am going to need a 220V outlet for the radio.