Correct. You can get the same power with half the voltage by doubling the current.
The trouble is the wires. A given wire gauge is limited in its ability to conduct current, not power. So if you double to the current, you'll need to have roughly twice as much copper in your walls, in your fuse panel, in your appliance, etc.
Additionally, losses due to heat are proportional to the current. If you double the current and halve the voltage, you'll lose twice as much power by heading the wires. For just a house, this isn't a lot, but it's not zero.
This is why US households still have 240V available. If you have a large appliance that requires a lot of power, like an oven, water heater, dryer, L2 EV charger, etc, you really want to use more voltage and less current. Otherwise the wires start getting ridiculous.
This is not to say that higher voltage is just necessarily better. Most of the EU and the UK in particular has plugs/outlets which are substantially more robust and difficult to accidentally connect the line voltage to a human. Lots of people talk about how much safer, for instance, UK plugs/outlets are than US plugs. If you look at the numbers though, the UK has more total deaths per year to electrocution than the US, despite the fact the US is substantially more populous. This isn't because of the plugs or the outlets, US plugs really are bad and UK plugs really are good. But overall, the US has less deaths because we have lower voltage; it's not as easy to kill someone with 120V as 240V.
So there's a tradeoff. There is no best one size fits all solution.
This is a very well written comment overall, but the energy loss in the wire is even worse than stated!
By modelling the wire as an (ideal) resistor and applying Ohm's law, you can get P = I^2*R. the power lost in the wire is actually proportional to the square of current through it!
Therefore, if you double the current, the heat quadruples instead of doubling! You actually have to use four times the copper (to decrease resistance by 4x and get heat under control), or the wasted energy quadruples too.
Crucially, voltage is not in the equation, so high voltages - tens or hundreds of kilovolts - are used for long distance power transmission to maximise efficiency (and other impedance-related reasons).
I was also surprised to read that heat is proportional to the current. In addition, increasing the temperature also increases the resistance in the conductor (Cu). It's around 0.4% per 1C for Cu, around 20% more heat at 70C.
Not sure about US, yet some high current lanes (thinks of threephase ~400V x 36A; IEC 60502-1) in the households are actually made of Al, not Cu. They tend to be underground though, the wires in the walls are still Cu.
Silver wire is used for some things, but it is a lot more expensive than copper which rules it out for most applications.
Here is a table of the conductivity (in units of 10^7 S/m), the density, and the cost of copper (Cu), aluminum (Al), silver (Ag), and gold (Au).
Cu Al Ag Au
Conductivity 5.96 3.5 6.3 4.1
g/cm^3 8.96 2.6 10.5 19.3
$/kg 9.03 1.2 1030 92100
If we had a copper wire with a specified capacity in amps, here is what aluminum, silver, and gold wires of the same length and capacity would weigh and cost as a percentage of the weight and cost of the copper wire, and what their diameter would be as a percentage of the diameter of the copper wire.
Weight Cost Diameter
Al 49 7 139
Ag 110 12646 97
Au 310 3190000 121
In 2017, there were 13 electrocution-related deaths in the UK. In the US, there are between 500 and 1,000 electrocution deaths per year. This translates to 0.019 deaths per 100,000 inhabitants in the UK and between 0.149 and 0.298 deaths per 100,000 inhabitants in the US.
Note that there is 240V in every US home. Low power loads run from a center tap 120V circuit. Also I wonder if people manage to electrocute themselves on "high voltage" circuits (typically 7.5KV) which due to the 120V thing have to be run everywhere so are more available to the casual electrocutee. In the UK although there are high voltage transmission lines, they terminate at substations, are often buried at that point, and there are high fences make it hard to electrocute ones self. E.g. a guy around here managed to electrocute himself very badly (but still survived) out in the woods by touching a bear that had itself become electrocuted by a live unprotected 7.5KV line.
Your deaths claim surprised me. AFAICT England has ~10 deaths by electrocution per year. The US has ~100 domestic electrocutions and even more occupational electrocutions.
How many of those deaths are attributable to electrical plugs, though? Given the US CPSC report at [1], I suspect that most of them aren't - in fact, one of the leading causes of electrocution deaths is "fractal wood burning".
The trouble is the wires. A given wire gauge is limited in its ability to conduct current, not power. So if you double to the current, you'll need to have roughly twice as much copper in your walls, in your fuse panel, in your appliance, etc.
Additionally, losses due to heat are proportional to the current. If you double the current and halve the voltage, you'll lose twice as much power by heading the wires. For just a house, this isn't a lot, but it's not zero.
This is why US households still have 240V available. If you have a large appliance that requires a lot of power, like an oven, water heater, dryer, L2 EV charger, etc, you really want to use more voltage and less current. Otherwise the wires start getting ridiculous.
This is not to say that higher voltage is just necessarily better. Most of the EU and the UK in particular has plugs/outlets which are substantially more robust and difficult to accidentally connect the line voltage to a human. Lots of people talk about how much safer, for instance, UK plugs/outlets are than US plugs. If you look at the numbers though, the UK has more total deaths per year to electrocution than the US, despite the fact the US is substantially more populous. This isn't because of the plugs or the outlets, US plugs really are bad and UK plugs really are good. But overall, the US has less deaths because we have lower voltage; it's not as easy to kill someone with 120V as 240V.
So there's a tradeoff. There is no best one size fits all solution.