This is not quite the same as the median: it is possible for the bottom 50% to improve but for the median to stay the same (i.e. imagine if everyone in the bottom 50% suddenly equaled the best of them). But the median is a lot better than the mean for not being distorted by large changes in the top and bottom percentiles.
This seems to tacitly assume that the outliers on either side have equivalent weight with respect to whatever is being investigated, while the explicit premise behind this proposal is that in this case they do not.