"Quicksort is already implemented a thousand times, so there's no need to implement it again, just find which library you need."
Yes, that's true, but we're talking about education here, not building websites.
Also, knowing about QS implementations lets you know when it's been done wrong.
Case in point: Microsoft's C runtime library shipped around the time of Windows NT and Visual Studio 6 had a sub-optimal qsort implementation - it took 97 seconds (on a 600MHz Athlon) to sort 260,000 integers with a constrained set of values (0-180), whereas other implementations (eg Numerical Recipes) could do it three orders of magnitude quicker.
Delving in, the qsort() algorithm didn't exchange elements where the value equalled the partitioning element, which leads to increased comparison function calls (effectively proportional to 1/range).