Of course in the real world for problems where sorting is actually the bottleneck and not just something you want not to kill your app's performance, you end up with things like timsort that destroy all these in practice.
Timsort is your first choice.
If sorting became a bottleneck, I'd literally look at every possible approach to speed it up that I could find before considering improving the sorting algorithm. Starting with trying to figure out how to throw around less data while trying to solve the problem.
Do you really want your business critical sorting rely on something that only might work?
Sorting algorithms are like crypto, don't roll your own if you can avoid it.
Not only that, I ended up being able to do it lazily making the user experience much better.
However the fact that sometimes we are forced to our last resort doesn't change the fact that we should be aware that it really is a last resort.