The argument doesn't quite work, though, because if you start to extract additional value from an animal then it becomes more valuable to farm/fish, and more of those animals get killed.
In the case of cod, cod is one of the most over-fished fishes on the planet. The extra money that the big fishing companies get from selling the liver separately certainly contributes some percentage to that over-fishing. (Some cod is sustainably farmed, but it's the minority.)
Your arguments are valid, so the truth is that none of the sources of omega-3 fatty acids that are the best choice now are good enough for the long term.
Nevertheless, eating a small quantity of animal food for covering the requirement for omega-3 fatty acids is still a great improvement over eating a large quantity of animal food containing other kinds of fat, which is better obtained from vegetable sources. Therefore, except for a little fish oil, I do not eat any other kind of animal fat.
I still hope to live enough to see improvements in the techniques of culturing unicellular organisms that can produce omega-3 acids, so that their oil will become cheap enough to replace the other sources, like oily fish, cod liver or pig brains.
In my opinion, in the distant future, the final solution to the food problem will be to have some genetically-engineered organisms, either derived from some parasitic plants, or derived from some fungi, able to produce edible parts mimicking all the foods that exist now, from apples or bananas to pork or beef meat, when fed only with minerals and with a simple organic substance, such as sugar or glucose, or maybe one as simple as ethanol, as the energy source.
Such genetically-engineered organisms would be grown indoors, possibly under ground, to save space.
The fixing of carbon dioxide into a simple substance like sugar and of dinitrogen into ammonia, would be made separately, in some devices using the energy provided by solar cells, which would cover much of what is now agricultural land.
Such artificial devices using solar energy to convert CO2, N2 and water into sugar, ammonia and free oxygen, could have much better efficiencies than the existing plants (though a lot of improvements over the existing technologies are needed to reach such a goal).
On the other hand, for the synthesis of the complex organic substances that are needed for our complete food, no methods better than those used in living beings are known yet.
In the case of cod, cod is one of the most over-fished fishes on the planet. The extra money that the big fishing companies get from selling the liver separately certainly contributes some percentage to that over-fishing. (Some cod is sustainably farmed, but it's the minority.)