I don't know nearly the same as the people here but maths is a strong point so I thought I might give a lay opinion.
The crux of your argument is that with a balanced system, everything will be fine. That is true, but you must look at the different weighting on each of the variables in the equation. Since the system is "balanced", if one variable is increased on one side, the corresponding variable on the other side must be matched.
For example, if 5 + 2x = y
If x = 1, y = 7.
However, if x = 5, y = 15
I think the main idea is that the equation doesn't balance most of the time. Most of the time, the level of inputs (ie waste), will never balance with carbs and
O2. Due to the imbalance, excess
DOC will hurt your fish.
An analogy, imagine you lived in a fully sealed glass cube. You are continually pumped with
CO2 from an exhaust, but have trees and other flora to "balance" it out. Although (simply)
CO2 + plant life =
O2, the flora cannot convert fast enough the
CO2 (waste) to
O2 ("clean" water), building up the
CO2, until it becomes toxic.
This also applies to why, for eg, 10 neon tetras in a 20g tank will need less
PWC than 10 goldfish in a 20g.