Great point. In the above example, if we included the scales, the numbers would be
Coffeeshop A: 4.5/5, 68/100
Coffeeshop B: 3/5, 75/100
For the geometric mean, when multiply the numbers and take the root, the numerator is the same whether we include the scale as the denominator or not. For the arithmetic mean it is not the case, as the numerator changes if we include the scales as the denominator, since to add we need a common denominator.