Well, it kills 1000+ people per year in electrical fires in the USA alone. We would never allow electricity in homes like this if it were invented today.
> Such a system would need a box in the basement and lots of seperate wires to outlets.
Yes. But if high voltages can safely be used, and the system is safe in case a cable gets chafed, then the wires become super thin like headphone wires, and overall, the whole system could be produced cheaper than existing systems which use a lot of copper and plastic.
Fire is eliminated too, because a high tech solution measures power losses at every connection, and as soon as enough is unaccounted for to possibly be heating something up to the point of a fire, it switches off.
The main disadvantage is that every appliance or device needs circuitry to measure power flows. This is mitigated by the fact that voltage is variable - low power devices could simply run off 5 to 20 volts at sub-1-amp and not bother with any fancy measurement. Only high power stuff would need the high voltages and all the safety circuitry.
I suspect the risk of fire very thin wires and AC voltage is fairly low - the wires will burn out before there is much of a fire risk.
The current system is nice and flexible and simple enough to be safe. Extension cords work well when you are plugging in a bunch of usb devices and tv/laptop/console. But you can also use the same outlet for a hair dryer or a mixer. Higher current devices like ovens, showers, and cars need to be treated seperately to prevent unsuitable parts adding a fire risk. Lack of compatability to domestic appliances is a feature.