Also, to save any further puzzling: In practice the very fast sort you use, even if it is labelled "Quicksort" probably doesn't actually do this "all the way do

Also, to save any further puzzling: In practice the very fast sort you use, even if it is labelled "Quicksort" probably doesn't actually do this "all the way down" even though that's the strict algorithm. They'll have a highly optimised small sort and use that whenever sorting very small things. So e.g. IPN Sort the Rust stdlib unstable sort will do this for 16 items, even though for a big slice it'd quick sort them by default, once it's down to say 10 items they're going to the specialised small sort. Any serious "fast" sort in 2025 will be a hybrid, using several of these classic sorting algortihms, plus other insights to produce the overall best solution to their problem on modern hardware.