We can't easily select better pivots for quicksort. For every deterministic selection of a pivot based on a fixed number of elements, a case can easily be constructed which will demonstrate its descent into quadratic behavior.[1]
In order to select a "good enough" pivot for quicksort, you can't just examine 3 elements or 5 elements or 10 elements; you must examine 0.5N elements or 0.25N elements or 0.1N elements. If you pick the median of that subset of elements (which you must do in linear time, mind you! Have you read CLR's "median of medians" algorithm, the one you have to use because quickselect doesn't guarantee linear time?) then you're guaranteed to complete in O(n log n) time, but at what cost? You've massively increased both the complexity and the constant factors of your solution.
[1] http://www.cs.dartmouth.edu/~doug/mdmspe.pdf is one example of how to do so.