Your feet are your interface with the ground. As such, I'd imagine the benefits of strong feet are:
1. ground contact should be more stable and balanced which is important when applying maximal force.
2. the toe-off should be more powerful because the muscles of the feet are stronger.
3. the transmission of force from the big movers (glutes, quads, hamstrings, etc.) to the ground should be more efficient because the interface through which that force is being applied is more rigid and stronger.
ELITETRACK Founder