It's more to do with the fact that std::sort's definition is visible to the compiler and qsort() is not.
Put qsort() code in stdlib.h, make it static and write a static intcmp() and you'll see the compiler inline that no problem.
You could do some macro magic instead of templates e.g. `DEFINE_QSORT(int, intcmp)` which could stamp out `qsort_int` but that's not a part of the stdlib.
C++ arguably gets this right since sort<int> and sort<string> will be separate functions, although templates are of course a footgun. And of course duping the logic for std::sort<T> for a bunch of different T impls increases the binary size.
When this is done, the compiler can inline qsort, and replace the indirect function call with an inlined version of intcmp, and then things are equivalent.
In that case, the compiler could make a specialized qsort using intcmp automatically.
In my similar experiments with std::sort with a function pointer only gcc does this with -O3.