Interesting argument... I've no concrete answers to this, but here's my take.
There is a flaw in the later part of your theory. There is a reason we measure by ppm and not by absolute amounts. Plants need a certain concentration of each nutrient in the water to be able to absorb the nutrients via osmosis or similar process (any knowledgeble ppl can enlighten us with the actual process?)
So, yes, in a smaller tank, the NO3 levels drop much faster and you must dose more often to maintain the required concentration levels. Thereotically, you can dose more to create a reservoir effect, however experience in the hobby indicate that too high levels of NO3 and/or PO4 can contribute to algae problems. (Some forumers have had no major algae problems though with levels much higher then recommended)
There is also the concept of "critical concentration" or something like that. I think FC can shed more light on that. From my limited understanding, that's the minimum level of a nutrient's concentration a plant requires to be able to absorb the nutrient from the water. So while you would raise the NO3 levels to 10ppm after a water change, you can let it drop to about 5ppm before topping up to 10ppm again.
The general explanation given to explain why large tanks are more stable is their ability to buffer changes/errors/neglect better. You partially explained it in your argument. Nutrient levels probably maintain their levels better/longer in large tanks.
Consider also dosing variance. Assume you dose 5ml per 100l using a measuring cup and an approximation error of +/- 1ml. For a 100l tank, that's an error of +/-20%. For a 500l (25ml) and 1000l (50ml) tank, it's 4% and 2% respectively. This applies to dosing everything from baking soda (to raise KH) to CO2.
Large tanks also buffer temperature changes better. Temperature in a large tank takes a longer time to rise and drop. Temperature in different parts of a large tank probably varies more between areas, which may explain why some shrimps can take 30 celcius in a large tank better then in a small tank (i.e. shrimps in the large tank simply retire to a cooler parts of the tank, while in a small tanks, there are no significant cooler part to escape to).
If we look at the actual numbers, some ppl may conclude that the absolute differences may not make a big enough difference to affect the stability of the tanks. (E.g. so what if I raise NO3 to between 8 to 12ppm in a 100l tank vs 9.6 to 10.4ppm in a 500l tank with each dose? Does 2ppm make that much difference?) Perhaps it's the frequency combined with the size of the variance that makes a difference?










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