On one hand, your point seems to be technically correct.
On the other hand, don't we average things that we can't technically justify all the time? Teachers give out homework and tests, assign a weight to each homework and each test, and average the results to assign you a grade. Is that grade arbitrary? Yes. Does that mean it is useless? Probably not.
If I were you, I would make your case based less on "you can't do that" and more on "if we used this approach to aggregation, we would improve our ability to detect cases X and Y that our customers really care about".
On the other hand, don't we average things that we can't technically justify all the time? Teachers give out homework and tests, assign a weight to each homework and each test, and average the results to assign you a grade. Is that grade arbitrary? Yes. Does that mean it is useless? Probably not.
If I were you, I would make your case based less on "you can't do that" and more on "if we used this approach to aggregation, we would improve our ability to detect cases X and Y that our customers really care about".