A binary search tree built from sorted input degrades to a linked list, and the fix, AVL or red-black, adds rotations to every insert. Why accept that overhead?

A. Because it turns an average-case hope into a worst-case guarantee

You are buying a guarantee, not average speed, sorted input is common rather than exotic, and an attacker can supply it deliberately. Paying a constant factor on every insert to remove an O(n) worst case is the same trade as randomised hashing against hash flooding.