I guess potatoes would eventually disintegrate completely and just make the soup/stew a bit thicker. But yeah, soggy noodles sound unpleasant - but when the perpetual stew was actually in use hundreds of years ago (in Europe), noodles weren't really a thing yet...
I used to add cream of mushroom (found in cans) to the soup, because I really needed the calories. It really thickened the soup and did pretty well. You can also just add corn flour (pre-mixed in a water before) and it thickens up the soup easily.
If I consume 1/3 of a well mixed soup every day and top it up to full, then in a week, only about (1/3)^7 = 0.05% of the first day stuff remains. You don't really have to worry about the longevity of the ingredients.