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).
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.
Cu is more conductive than Al so an Al wire has to have a cross section area about 1.56 times that of a Cu with the same current capacity.
But Cu is also denser than Al so the Al wire is only about 0.47 times the weight of the Cu wire.
Al is is much cheaper than Cu so the Al wire is only about 13% the cost of the Cu wire.
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
Weight Cost Diameter
Al 49 7 139
Ag 110 12646 97
Au 310 3190000 121[1]: https://www.cpsc.gov/s3fs-public/Electrocutions-2011-to-2020...
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.