Reno, I don't understand your explanation.
You've described 200 A flowing in each wire, but in fact, the 200 A would be divided between the two according to the ratio of their impedances.
Given your example, that ratio is (.0194 / .00967) = 2:1, so 133 A of that 200 A would flow in the 2/0, and 67 A in the #2. The voltage drops therefore are equal, and there's no power "flowing" from one wire to the other.
Argument #2: A 2/0 wire is made up of 19 strands. Isn't that the same as an 18-strand wire in parallel with a 1-strand wire?