Performance. Internal representation. You are not actually modifying things in place. Those are the equivalent of linked lists not arrays. That quicksort is not quick at all because the append operation in Haskell is linear. You can't use those lists to implement quicksort.

Haskell is lazy. a ++ b === (head a) : ((tail a) ++ b) (plus the base case)

It is only linear when you force it to evaluate, which ideally happens only once (amortized) in your program when the result is consumed. As long as you are careful, you don't get the bad quadratic performance that you'd get from something like eagerly appending a character to a string in a loop in Java. There are either gotchas, though, including relying on the compiler to do things in constant space that naively look linear, and also knowing when the compiler won't help you and you have to structure your computation manually.

“Modifying things in place” is, from the logical standpoint, an unnatural and even dangerous thing. A person that is not familiar with (imperative) programming often has a hard time understanding variables and assignments (similar to some programmers not understanding pointers). Mathematics doesn’t have assignments, either. That should tell you something...

It mostly tells me that mathematics does not care about runtime or space performance. Which is fine, because mathematics is about solving abstract problems, not getting a Turing machine to solve concrete problems.

In that case, quicksort requires danger and artifice. In any case, it's not quicksort.