If the water could not gain speed on the way down it would stand still at the top of the mountain. Put gravity into the equation and the water gains speed.
Thanks to pipes, the potential energy is not converted into speed on an open ramp along the slope of the mountain, it is converted from pressure to speed right at the turbine station. Any inertia within the pipes is just a medium for the pressure transfer, much like the inertia of a spinning axle in a mechanical transfer of torque. It is there, but it is not the driving force.
