That's true, but it's also worth pointing out that the worst case can be trivially prevented by shuffling the array before you Quicksort it. Which is maybe a confirmation of your larger point.
In the average case you do the expensive median of medians on a small fraction of the data and so only pay a few percent average penalty. And in the worst case you still get n log(n) performance.
Of course, shuffling is still potentially helpful because ascending/descending order is often common in many applications.
What changes is that one very common permutation of data (ascending data) does not have O(n * 2) performance.
I'm not sure what you mean by deterministic shuffling. Shuffling is supposed to be random, and therefore non-deterministic. In practice, you'd probably use a pseudorandom function to implement shuffling, but the goal of pseudorandom functions is to be indistinguishable from random functions, so that detail shouldn't matter.
Probably what you meant was that shuffling makes the worst case very unlikely.
On a practical level, if you have to shuffle the data before sorting to make your sort algorithm work better, you've most likely already blown any performance advantage. So you might as well choose a different sort algorithm.