It’s a common thougt that doubling the voltage to 240V just automatically makes everthing cheaper and more efficient. You are right that reducing the current load significantly minimizes resistive losses in the conductors and reduces the size of the wiring required for the same power draw. That is the main selling point. However, the savings aren't just about the copper wire. When you switch systems, you have to account for the entire apparatus. You will need new circuit protection and heavy duty service equipment, meaning the upfront hardware cost isn't zero. Furthermore, load balancing becomes a major consideration, especally if you aren't running appliances that naturally require that higher voltage.
If you are planning this, start by mapping out all your current loads. Figure out what the maximum expected current draw is before sizing any new service entry points. Running the new configuration is all about correctly sizing the amp rating for the main breakers before doing any major cuts or runs.