Good point and you're not wrong. One mitigating factor is that resistance isn't constant: In copper it increases with temperature, and I^2R causes temperature to go up, which causes resistance to go up, and you get something of a positive feedback loop. Temperature rise is one of the main reasons why standard wire gauges are specified the way they are.

If you use 4x higher voltage, the temperature rise is much less significant (16x less significant to be precise) so it becomes more or less a non-issue and you can treat resistance as a constant.