In normal situations, you would not lose half the energy, or hydropower would be totally bunk (actually maybe not, considering the efficiency of burning fossil fuels…) But in this degenerate case, you cannot ignore the losses.
In a hydro power plant, the water turbine constitutes the "friction" so, if there were no other losses, the half of the energy "lost" from the system is precisely what your generator gave you.
Are you sure? I was going to add that the intuition comes from demonstrations we might have seen, where in a series of tubes, regardless of shape, water will be at one level. As in this picture:
