They do, to a degree. Modern implementations generally use hardcoded routines for very small numbers (say, up to 5), then some quadratic sort like insertion sor

They do, to a degree. Modern implementations generally use hardcoded routines for very small numbers (say, up to 5), then some quadratic sort like insertion sort, then quicksort. The dispatching can happen at all levels of the recursion, so quicksort's leaves are actually optimized sorts for small collections.