Studies show we still are.
To be honest I don't know how people lived in piscatorial villages, my grandmother lived near a river and they only had fish twice a week.
Fishermen were probably subject to the same constraints, of selling their products and probably worse since farm animals can be kept alive untill sold or eaten and fishing on high sea is among other things dangerous, everything adding to the cost, and fish doesn't last long, so it had to either be consumed shortly after or it had to undergo a drying process, and since everything that involves more work involves more costs, selling was probably better.
Regarding shellfish in pre refrigeration days, don't know how it worked, it can be lethal if not eaten fresh.
Don't know what it means going off -grid in nutritional terms, but considering that wild herbs have been the food of last resource in rural areas, the opposite looks true, in fact in extreme situations people tend to survive on plant only diets.
So one may ask what exactly was the nutritional meaning of animal products in rural societies.
Meat once a week at most, in some cases in festivities only, in others never, looks negligible.
Dairy seems to have been consumed more regularly, but in modicum amounts. For what purpose? It's not that high on protein in particular if one is consuming it in very small amounts. Maybe fat is the answer, even in the region of olives, olive oil was still a delicacy in the old days.