Why do rivers near active faults erode faster than rivers far away?

Answer: Faults create a damage zone

Faults are just thin cracks — Wrong. While faults are often drawn as lines on maps, the rock around them is not pristine. The erosion signal extends far beyond the visible crack, so this picture is too narrow.

Faults create a damage zone ✓ — Correct! Active faults fracture the surrounding rock over a wide zone, creating a 'damage halo' that can extend tens of kilometers. This broken rock erodes more easily, so rivers in the halo cut down faster than rivers farther away.

Faults heat the river water — Wrong. Faults do not heat river water enough to affect erosion. The main reason for faster erosion is mechanical: the rock is shattered and weakened by fault movement.