Averages are formulated as measures of centrality in the L2 norm ("straight line" distance), sum(values) / count(values). Quantile regression uses modifications the L1 norm ("city block" distance); if median (50%) then it is a measure of centrality. Not everything is an average. If you're interested, this is a good (but math heavy) treatment: https://en.wikipedia.org/wiki/Quantile_regression#Computatio...
Innovations like these are more about ‘shocks’ that surface fitting cannot capture.
Note universal approximation theorem applies only to smooth surfaces.