I think what OP is trying to say is that aquarium volume vs plant volume matters. I've never heard of this or seen it proven but it is a novel idea. My biggest defense against this mattering is that ppm is ppm. It doesn't matter how big the tank is, the ratio to fertilizers running over the leaves is still the same if the ppm is the same, no matter the tank size.
What could change that? If for some reason the length of time between fertilizers running over plant leaves matters (due to more water between them). I'm not sure what else a larger aquarium volume vs plant volume would effect.
What I completely disagree with is this:
Therefore, it may become more difficult to maintain "low nutrient" systems in these smaller tanks because your plants will bottom out on nutrients faster when compared to taller tanks.
This makes no sense. If there are 3 plants in a 20 gallon and 6 plants in a 40 gallon with fert ppm being the same, total mass
(the raw tsps) of the fertilizer floating around likely doesn't matter. Put another way, putting 3 tsps into 20 gallons and 6 tsps into 40 gallons doesn't make the 20 gallon tank any worse off. The ratios remain the same.
NOW, if you have 6 plants in a 20 gallon and 6 plants in a 40 gallon, that will cause a fert requirement difference. So again, I think we need to talk about aquarium mass vs plant mass. I think OP is getting lost a bit.
And finally, if you are reading this and still not following, think of it this way: a gas engine needs gas to run. It sucks down gas at a certain rate to do that. Everytime you add a new plant to your aquarium, you just added another gas engine. More plants = more fertilizers required. Tank size has nothing to do with this unless you mashed a [censored][censored][censored][censored] ton of plants into a 10 gallon so much so that they take up more space than the water. Then we could be talking about a nutrient transfer issue due to flow, etc.
If you normalize fertilizer rates W.R.T. plantable surface area, there is a large discrepancy between tank sizes. This may be particularly important for nutrients we maintain in low levels i.e. in nitrate limitation, trace nutrient dosing.
For example: in a tall tank that is densely planted, dosing 2ppm nitrates each dose you will probably have sufficient nitrogen. In a tank of equal foot print that is planted to the same coverage but is half as tall, 2ppm nitrate could become insufficient. This effect could be more significant for nutrients we add in the ppb range.
No... why would this matter? The same amount of plants are touching the same amount of fertilizer in both scenarios. What you might mean is that the plants will suck up the nutrient faster in the smaller one. That makes sense.