Optimizing a propeller for wide speed range is practically impossible. As long as you can not vary the blade twist or the blade chord, there is only one combination of airspeed and propeller speed at which the full blade operates at its optimum angle of attack for the selected airfoil at that radial position. At the tip the blairfoil has to be very thin for mach critical number reasons, at the root it has to be very thick for structural reasons. Accordingly the best l/d for each radial position is at a different lift coefficient and hence at a different angle of attack requiring a specific local blade chord.
The next restrictive parameter is the torque curve of the engine, it does not help to have a lot of torque available at low speed, if the propeller can not accept that torque, as it is approximately increasing with the square of propeller speed. Almost no engine has such a speed ^2 torque curve. So if shown in a torque over speed diagram, the intersection between the propeller curve and the engine curve happens with a lot of angle (up to perpendicular), hence you need to change the curves a lot to move the intersection point on the speed scale, this means you can only change propeller speed while significantly changing power. This restricts you to a very small speed range in which you can reasonably operate the propeller.