For example do quickselect on 9/10 rounds but on every 10th round do a median of medians. The overhead of guaranteed performance will only be a few percent off of the average.
I'm not saying that it's impossible to do it and always will be. Re-read what I've said if you like, and you'll see I am simply sharing an anecdote for the purposes of an analogy about this particular situation.
It's a hybrid of quickselect and median of medians, but the switching strategy's a bit more complicated.
But basically both quickselect and median of medians are divide and conquer. Median of medians is an expensive way to guarantee a good division. Quickselect hopes for one.
If quickselect goes well, then median of medians will be relatively cheap when run because it is run on a much shorter list. If quickselect does not go well, the median of medians passes guarantee progress. So average behavior is only slightly worse, and worst case behavior is still nicely bounded (albeit with a much worse constant).