Because if the larger envelope is changed to contain four times as many dollars, then /2 vs. *4 points back towards swapping indefinitely.
If one envelope contains 4 times the money of the other envelope, then by swapping you either gain 3x or lose 3x, where x is the amount of money in the smaller envelope. Even in this case, the average return is +3x -3x = 0.
It is, it's the one where you treat both as having the same expected value
that the expected value is the same that is an outcome of all solutions, so just stating that is reductive.
What is at question is the reason for getting to the expected value is the same.