We always hear about the reactive effect as being a spring like movement etc, but let's talk about a countermovement jump vs a paused jump. A countermovement jump will usually be higher.
In my opinion, the only real difference is not a spring like effect of any kind, the only difference in reality is the fact that the muscles get loaded more because the body weight increases as you lower and stop yourself from lowering.
The same thing occurs in a high vs even higher speed plant. The faster you go, the more strength you need to amortizate your body because your bodyweight * acceleration (plant speed) = the total amount of weight that needs to be amortizated. And if you can take in that weight, the muscles (previously enabled eccentrically to stop you from crushing into the ground) remain activated for the concentric part of the movement too, if it's done quickly.
I think that's all there is to it in reality. I keep on hearing about all this "spring" thing and I think that's erroneous and makes people fail to understand the real thing that is going on.
Now the only counter-example to this is the Olympic lifter that jumps a lot from a standstill and sucks coming off a run. I think in that situation it's a matter of technique (where technique = failing to understand/apply the proper body position to produce the maximum amount of force, and to be the most easy to amortizate, from). Also, the adaptations over time for the O-Lifters require them to generate "standstill" acceleration from a horizontally neutral position, hence their preferred "stopped" position for developing power.