A-J, the psoas works in generating hip flexion, so it’s working when we’re driving the leg up. As for why hip flexion is so important, that’s a bit tougher to answer.
One line of reasoning is that strong psoas muscles, combined with equally strong abdominals, could facilitate better/more efficient front side mechanics. With strong hip flexors and abs, the trail leg will not trail behind the body as much, and this point leads to two more sub-points.
Sub-point one is that stopping excess backside mechanics will put one in better position to run at top speed. If we look at the greatest sprint performers of this era (Bolt, Powell, Gatlin), the one thing that really stands out is amazing front side mechanics.
And sub-point two is that eliminating the backside mechanics will mean the legs are cycling over a smaller ROM. Since that’s the case, there will be more air time in each stride where the muscles aren’t contracting. During this extended air time, the body will have slightly more time to regenerate ATP and therefore running efficiency will be improved and endurance will rise (ie. you’ll be able to sustain higher speeds for longer periods of time).
The other line of reasoning is that during acceleration a powerful hip flexion will lead to a powerful hip extension of the opposite leg. There’s a thing called the inverse-extension reflex, and it makes it so when one leg is forcefully extended, the other other leg is forcefully flexed and vice versa. In this way, a more powerful hip flexion during either top speed or acceleration would lead to a stronger reflex-potentiated hip extension of the opposite leg.
And Goose, pretty much regardless of what muscle group is being trained, heavier weights and intermediate reps (think bodybuilding) are the best at generating hypertrophy. Therefore sets of 8-12 of weighted decline situps would probably be the fastest way of enlarging and strengthening the psoas.
Excellent point. My experience has been that the imbalance of these two causes plenty of problems with efficiency, which in turn leads to injury, eg. hamstrings.