The position might be useful, if you have a second list with some side data stored in it, and not a list of tuples :).

I had the idea to file a bug, when I had a list of coordinates and wanted to use the point with the median of the x-coordinates as "representation" for the dataset. With max() and min() in mind, I used median_low() with key argument and get the error that key is not a valid argument (my solution was to use dicts then).

So I thought this would be a similar use case as max() and min() and in fact more consistent. But I fully understand your concerns, that this breaks consistence with the other statistic functions.

This is not a killer feature, but in my opinion nice to have, because it changes nothing on the default (expected) behaviour, but provides with less code very high flexibility.

I cannot say something about other languages.