You are wrong.  The amperage is split in half because there are 2 hot conductors in 240v wiring instead of there only being one in a 120v feed. You are still using the same amount of power.  Watts is Watts.  You cant defy ohms law.   A 120v circuit drawing 20 amps is 2400w and a 240v circuit drawing 10 amps is still 2400w.

Power = E x I (Voltage x current).

So you are using the same amount of power no matter which route (120v or 240v) you take.  Indeed the amps is halved ON THE POWER CONDUCTORS of a 240v wire feed but that wont help since most houses have 120v feeds so a 240v would have to be installed new and obviously could be sized CORRECTLY to avoid any overheating for constant duty.