I suspect that the reason fish don't become magical "freshness points" when put in the fridge is because, unlike tomatoes and pole beans, they have new meals associated with them.
The bass become "Bass with Squash", the catfish is "Blackened Catfish" and the trout is... uh... something trouty. You can only make a fish dish when you have some fish available, and when you make a fish dish only the fish is removed, rather than a fish plus food points or fresh food points.
I don't put that much effort into stocking the fridge with food so this hasn't bothered me much. Instead of paying attention to food stock I pay attention to the leftovers in there... if there's only a plate or three left and a sim with cooking skills has a couple "hours" of free time, I have them serve a meal or two, take all the plates and put them in the fridge for everyone else to eat. If there's fish around, yay!, I use it. If not, oh well, mac and cheese with strawberries it is.
If you really needed to know how many fish were in there... maybe use them all up so you know you start at 0, then after that ONLY restock in groups of say, 10 fish... then don't let yourself restock again until you can't make the "Blackened Catfish" anymore and then you know you have 0 again. You would always know you have between 0 and 10 fish, which would keep you from overstocking, but you might find yourself out of fish again at an inconvenient time so I dunno how much that would bug you.