As a propeller tip reaches the speed of sound, more and more energy goes into making more and more noise, and no improvement in thrust. We are, after all,
looking for more thrust. You dp get more thrust from the turbo prop on a
C-130 Hercules , but.....it isn't really practical on a Mustang.
I expect that a prop near mach one is experiencing cavitation ....a vaccuum
forming near the surface of the blades, and we know how an outboard cavitates near the surface and loses thrust. In jets, we go through a lot of trouble to keep the speed of incoming air below the speed of sound, utilizing a lot of fancy little tricks ie. the variable geometry nose cones on the SR -71.
There 's a lot going on with high tech areodynamics. Take your hat off to a few good men.
Best regards, Dan