Yes I do understand what you're saying since your very first post. I'm just stating that plants are great for stable tanks (just like the hypothetical one you mentioned), but not for overstocked because these tanks are never stable. Lets add another variable to this scenario - overstocked with a bunch of cichlids. After some time, the 14ppm nitrAtes per week in the hypothetical scenario wouldn't correctly indicate the total amount of pollution in the water.
Plants grow and consume more or less nitrAtes throughout the week (assuming that these plants are being maintained properly). Even after a few months, if the nitrAtes levels are 14ppm, how would we know the level of all the dissolved waste (unmeasureable with hobby test kits)? Is it dangerously high or is it at a safe level? If its high, then we need to do more water changes than normally. The 14ppm nitrAte is a great number. Its a fantastic reading that actually covers the true reading of all the other hundreds of pollutants in the water and forces us to guess the amount/frequency of water changes per week.
How about in a few months all the fishes grow and increase the bioload in the water. Witout plants, the nitrAte level in the hypothetical tank indicates multiple water changes throughout the week. With plants, the nitrAte reading tells us to do 1-2 more water changes per week. Over time, we can maintain better water quality with the unplanted tank more than the planted tank because we know the actual amount of pollution inside the unplanted tank and can make adjustments as needed.
Then what if the 2 biggest fish die a few weeks later? The bioload changes again and we are back to wondering how much/many water change we should actually be doing per week.
With a healthy number of stock in a tank, we know that the water change schedule never changes because we account for the full size and bioload of each inhabitant and plan to meet the minimum requirement them.