The air in front of the propeller (or a wing) has to start speeding up to go around the curvature. So the air will exceed the speed of sound before the propeller will the end result is inefficiency if that happens or in other words you are converting hp to noise. At altitude the speed of sound is less than at sea level.
So for take-off propeller speed around 650mph but at cruise around 450mph.
So you can only go so "wimpy" at the tip before the poor thing just flutters.
Of possible interest is NACA Technical Report 643 (done in 1938). It contains some tests of propellers similar to the planform of those designed by Paul Lipps. They gave slightly improved thrust at high speed, appreciably lower thrust at takeoff (and Lipps alluded to this his Contact! article). That would suit a Reno racer just fine, maybe not so good for more general-use acft.
Paul indicated the thrust for his props would typically be close to the same at climb airspeeds and better at top speed. For some purposes, that would be great.
There is a limit to how "pointy it can be when subjected to wind speeds of 650mph to 450mph. The "pointy" is less drag but also less strong. The other thing is "pointy" produces little or no thrust, you have to give something to get something and you are going to have to give some drag to get some thrust. Reasonableness.
The DC-6 does 315mph @ cruise @ 25,000ft. How pointy are those propellers? (13ft 6 inches diameter)
The "6" is also very fuel efficient when carrying 15 tons of cargo and is still viable today.
Are these Lipps-style prop planforms popular on planes with controllable pitch props (subject of the thread, I'd almost forgotten!) The rules require the racing biplanes to use fixed pitch props. The Lipps blades are plenty coarse, but at fairly close radius. Without the ability to change pitch, high RPM is the only way to keep these engines loaded up at high airspeeds (260 mph lap speeds). These racing biplanes see 3600 rpm,. Maybe the Lipps props are an answer for this particular highly specialized set of requirements. For other requirements, other props.
Say you divide the propeller up into stations, then each station "eats" a different amount of power, there is a fraction of total power available at the tip. Propeller diameter limitations and power available to drive the planform of the tip will dictate the chord at the tip. What are you going to do make the prop three foot chord in the center so no power is available at the tip so it can be pointy? The last approximately 1/3 of the propeller including the tip is the most efficient at least traditionally of producing thrust.
The Elippse propeller has chord at the tip? It has a shorter chord than the inboard station from it and that from the next and so on, this is a matter of calculation not a predetermined idea of "pointiness".
Many people "used to" before the government became more prevalent in Alaska bend the tips of their propellers forward, this reduced the vortices at the tips and less gravel/FOD was picked up so reduced rock dings in the propeller and the rest of the airplane. This is the kind of thing you'll do trying to save a buck and working off of gravel. Bending them forward is opposite the way Prince and others seem to do their tips but worked better for FOD reduction and speed was less of a concern. I wonder if a Elippse style of propeller would benefit from the tips being bent?