Briefly, the uphaul supports the weight of the pole, thus controlling its height. The elastic in the downhaul allows the uphaul to be eased slightly without introducing slack (which would risk releasing the loop from the pole ramp). The pole will not “sky” because the freedom of movement in the elastic is limited by the stopper knot, but in generally light airs the pole will indeed rise slightly in a gust if the stopper knot has not previously been at its limit, although the sheets will tend to counteract this upward movement. Neither will the pole bonk down onto the foredeck – there is never any need to slacken the uphaul that much, even to park the pole; just a few inches easing is sufficient for this. (I’m not quite sure what you mean about slack sheets in the first paragraph?)
For the pole height to be controlled by an inelastic downhaul working against an elastic uphaul the shock-cord would need to be strong enough to support the pole weight. It would then be difficult for the crew to lower, never mind park the pole – the uphaul would become tighter and tighter as the pole was pulled downwards, making it very hard to release the pole from the mast. Or the uphaul would also have to be made adjustable, introducing added complexity – two controls instead of one. (Conversely when the uphaul is the source of adjustment it can be slackened at will to free the pole, while the downhaul elastic neatly takes up any slack.)
I’m sure it is possible to rig such a system, but there must be a reason that it’s usually done the opposite way. Give it a try…