OK - you are looking at the problem from a system point of view - and of cause - its the way we should look at it. However - I have experiences of fresh water systems where - when nitrification and denitrification is in balance (the figures for both NH4 and NO3 is constant to each other during time) and still have seen a steady drop in pH that has to be compensated for through adding HCO3. I wonder if there is other factors in the fish, or pathways of inorganic C for the autotrophs. that contradict/work against the alkalinity formation inside/outside the fish when processing the food from a holistic point of view. I admit - I have difficulties to recognize such factors in freshwater but there is at least one important factor in saltwater fish that can make your calculations around alkalinity stability not be the whole truth in an holistic point of view.
For me - itthere is indications that at least the second stage bacteria in the nitrification process do not take up inorganic C directly as CO2. The nitrification process will totally halt in low pH - (rich in CO2) water but works perfectly in high pH (low CO2 content but more HCO3 content) It is also an experience for me that if you rise the alkalinity to around 2-3 in KH in fresh water (around 1 meq) and lower the pH with CO2 - nitrification works in spite of low pH - Is KH below 1 before adding CO2 - nitrification halt IMO. I know we have discuss this before - but it is still a paradox for me.
To start with fresh water fish - I have one experiences that indicate you are right - at least to some degree - according the total sum of alkalinity. I have been working with a lot of people with "crazy" ideas during my time here on earth. One of the more interesting experiences (according to this discussion) is a friends idea that if we did everything we could to inhibit nitrification and let the water accumulate NH4 - it could be a good way for a fish farm system. Its a well-known fact that low pH (read low alkalinity) both block nitrification and forming of toxic NH3. The idea was simply to keep the pH around 6.6 - 6.8 and have a heavy aeration in order the get CO2 out. The pH was stabilised through adding acids. The interesting thing in this was that we need to ad acids all the time because the tendency during time was that the pH rise. The fish was heavily feed during this time. This example will in my book talk fot your ideas. However after a while - We recognize that it was to risky. there was huge amount of ammonium concentrated in the water and slight rise in pH would bring a disaster and even to low pH could kill the fish. We use natural water with some aluminium in it and had one occasion of Al toxicity because pH get lower than 6.5 once.
However - is it the same for salt water fish in a holistic point of view ( Fish physiology and water chemistry as a whole system with interactions in different ways)
Let us assume that the fish secretes NH4 and therefore the increase in alkalinity takes place inside the fish in connection with digestion. A blood/plasma pH rise will result in a higher proportion of HCO3 that's need to be excreted in order to held blood/plasma pH constant. Normally - we assume that this happens in the gills - but saltwater fish seems also have an other pathway for HCO3 secretion that will lead to acidification in both blood/plasma and outside water. Salt water fish drinks and they need to handle the high concentrations of both calcium and magnesium in the digestive tract. At least in some saltwater species it has been shown that this problem is solved through secretion of HCO3 into the digestive tract and a following precipitation of calcium and magnesium to calcium carbonate and magnesium carbonate.
Here is one link
If we see this as a whole system - food - nitrification - denitrification - HCO3 secretion - calcium precipitation and so on - it may not be zero sum game in the end - at least not for salt water fish :)
Sincerely Lasse