The problem with fast, fairly high flying turbo-props with large propeller radii is that the propeller tips will be the first part of the aircraft to reach the speed of sound, with resultant significant loss of thrust for the power delivered to the propeller.
Compare the L188 Electra which was developed into the P3. The L188 was optimised to fly fast (about TAS 330 Knots) and reasonably high (F/L 250). The L188 had square propeller tips, with a slightly broader blade than the P3, i.e. the same propeller area to absorb the power. Some loss of aerodynamic efficiency was acceptable to avert the much greater loss of efficiency in having the propeller tips reach Mach 1.0 at fast and high cruise.
The P3 on the other hand was optimised to spend most of it's mission time at low level, where sonic propeller tips are not a problem, and the higher aspect ratio rounded tip propellers provided the optimum efficiency. It still left the P3 with a 'respectable' high speed / high altitude transit capability, but not in the same league as it's 'parent' L188. (This loss of high speed capability may have been compensated for in the increased power (by about 500 HP per engine) on the Allison variant fitted to the P3).
One of the prime reasons why many modern fast turboprops have 5 bladed propellers is to reduce the propeller radius, thus reducing tip speed and avoiding sonic speeds.