What do you think? Isn't the answer obvious? Look at any great single leg jumper at the time of take-off and you'll see a tremendous amount of hip hyperextension.
In fact, maybe that's one reason the "abs" (hip flexors) are pretty important in the one leg jump - being the antagonists of the muscles that do the hip extension, and because the hip hyperextension is the end of ROM in the hip extension movement, you want to have very powerful antagonists that are able to stop that powerful movement before it goes through "too much of a range" (too much hyperextension) and injures you. It's similar with the hamstrings stopping the quads from hyperextending the knee (in that case).
So the CNS has to be able to count on the strength of the hip flexors to stop that dangerous hyperextension from occuring, or else the CNS will cut short the amount of hip hyperextension that is going to be used, in order to prevent injury. So you won't get "max" hyperextension, meaning a lesser power/over a lesser ROM hip hyperextension, meaning a lower jump.
