Propeller design is a black art, usually incorporating moonlight seances, invocations to various dieties and human sacrifices. Having said that, many earlier (pre-composite/computer design era) props are only partly designed, the other part being a compromise between knowledge and production limitations, in my view. We've also managed to lose track of a lot of knowledge on how to design props for higher-powered engines once we switched to using gas-turbine engines without props.
When you look at 21st century prop design, you see that the trend is for blades to be scimitar shaped, with a more swept, narrow-chord bit near the tip as opposed to the inboard section. Essentially, this copies knowledge from high-speed wing design but it wasn't possible to build these props until we came up with composite blades in which we are able to counter the effects of blade drag and blade twist with strategically designed and applied material properties. For the engines under discussion, at that point in time there was a need for props to absorb more engine power, for which the immediate solution was to either increase the number of blades, or their span. Both are limited by either hub construction and complexity, or geometric limitations, tip speed and the associated loss of efficiency. They then had to move to increasing the blade surface by building broad chord blades. This then necessitates the use of a more high speed profile on the outboard ends and I think that the decision to use squared off tips is connected to either a construction limitation or the outcome from testing that pointed towards a higher overall efficiency from these tips as opposed to rounded ones. Sorry, not a very cohesive answer I'm afraid.