You're mixing up a distance with the measurement of that distance (or, in this case, a height with the measurement of that height). This isn't a fractal problem. Distances and heights are actual things, so there is a "right" height. The measurement of that height can and does have an error, but your claim was "There also isn't a 'right' elevation gain number." There is a right elevation gain number.

Not one of the common ones, but it's one that is built on the effort it takes to climb a hill. It uses power and speed data (among other things) to build up road gradient and then integrates gradient to get elevation gain. It can reliably and repeatably reproduce small changes in road grade. Better still, we can use the Central Limit Theorem to reduce error in the elevation gained when integrating the gradient.