This debate reminds me of pythagorean_expectation. This was used by Bill James in baseball. If I remember correctly, it does a better job of predicting future wins and losses than their previous season’s win/loss record. It states:
Pythagorean expectation is a sports analytics formula devised by Bill James to estimate how many games a baseball team “should” have won based on the number of runs they scored and allowed. Comparing a team’s actual and Pythagorean winning percentage can be used to evaluate how lucky that team was (by examining the variation between the two winning percentages). The name comes from the formula’s resemblance to the Pythagorean theorem.
I think you could reasonably substitute the number of runs scored and allowed for game wins and losses in a set. I am fine with either implementation of ELO, but I think both sides of the argument have merit.