I think the plant produces more roots when the nutrients are too low. Just like searching for water, they search for nutrient and need to grow bigger and increase their surface area to absorb enough nutrients. If the nutrients are the correct amount, the plant can put more energy into growing leaves, flowers and fruit, instead of roots. That is my thoughts/experience, would like to hear what others have experienced.

Chiles, at least, grow roots on their own schedule pretty much independent of nutrient concentration.

Is that Rapunzel going down the stairs?

Based on an experiment, I have noticed more dense roots when there is a lot more oxygen present, so that's one thing maybe my plants aren't getting enough O2. I'm sure there's a lot more factors.