Too much stress on the nervous system without being more effective than regular jumps as an activation tool.
Furthermore the long eccentric you mention (I assume that you mean waiting 2-3 seconds after you land before jumping) is only useful as a motor learning tool to learn to absorb force THEN jump. When using depth jumps to improve power the goal is to use the energy accumulation from the landing to produce MORE power in the jump. The result is that you should jump HIGHER when doing a depth jump vs, when you do a vertical jump.
If your depth jump is lower then the box is either too high for you or you are not yet efficient in that type of exercise (and the landing becomes inhibitory instead of potentiating). In both cases you need to drastically lower the height of the box.
SIDENOTE: I personally use a sensor called "BEAST" (thisisbeast.com) that measures velocity and power. So when doing depth jumps I start by establishing a power /speed baseline with a regular vertical jump then gradually increase the box height as long as I can produce AT LEAST as much power and ideally. I also stop the set when power drops down in a jump.
OK back to your question, a long eccentric/absorption phase will defeat the purpose of the depth jump, which is to produce maximum power by using the stretch reflex. After 2 seconds the benefits of the stretch reflex and accumulated energy is lost and the exercises loses a lot of its efficacy. On the other hand I'm not a fan (anymore) of rebounding up super fast either (imagining that the floor is hot)... the only thing that matter is the power produced and for most people trying to rebound as fast as possible will lead to less power production... the only coaching cue should be "jump as high as possible". Let your CNS pick the best strategy.