You can, of course, design a device which extracts energy from water by using the difference in the water's potential energy (i.e. a height difference) rather than its kinetic energy.
Practical hydro-power units make use of elevation difference (head, potential energy), since this is much more useful energetically than velocity (kinetic energy).
For example, to change the elevation of 1 kg of water by 1 m corresponds to a potential energy change of 9.8 J. To change the kinetic energy of that 1 kg of water by the same 9.8 J you would have to accelerate it to 4.4 m/s or 16 km/h, which is much faster than the typical flow velocity of a river, which would typically be only a fraction of that.
Therefore practical small scale hydro-systems (like water wheels) divert the water down a side channel while the river falls, and then let the water descend back to the river over the wheel, using gravity to do the work.
Well engineered hydraulic turbines can have a mechanical efficiency around 90%, so there are only marginal gains to be made by improving on this. Claims of a 3x improvement in efficiency would only hold water if the original efficiency was less than 30%, which is terrible by most standards.
In any hydro-power system, if the water leaves the apparatus at high velocity it is taking kinetic energy with it and therefore reducing the efficiency.