Comment by mapotofu

Pottery of the time was low-fired and did not generally reach vitrification, and it was not glazed with a silica-based glaze that would seal it.

So over time this pottery would absorb water. And especially low-fired bits could totally break down.

Source: amateur ceramicist, and I have first-hand experience with cone 6 clay (vitrifies at 1200c) bisc-fired to cone 04 (1060c) and crumbling to bits when left in water too long.

If you try to make a planting bed in any settlement that’s more than say 100 years old on a site that was continuously lived on, you are guaranteed to come across at least some shards of glass, pots, plates, etc. Even if the spot was never explicitly a trash mound. Things break, people usually try to pick them up and put in trash, but (especially in grass) miss pieces. When kids break stuff you often don’t want them picking up sharp objects. Things get stepped on and pressed into soil. Many many reasons to find pottery shards where they seemingly don’t belong.

A lot of these observations about the miraculous soil caretaking of the elder Native Americans are in all likelihood just "Look at this garbage dump, so fertile, such agricultural skill!"

Broken half-fired terra cotta is effectively unusable rock. Terra cotta is semi-disposable, so lots of potsherds are produced per person-year before plastics/glasses/metals are introduced. It's the single most common and best-preserved archeological artifact. Broken pottery was used in place of sand to stabilize the clay in new pottery, but other than that it doesn't have many special qualities.

I have thought about this and figured it was more mechanical (ie drainage) than chemical (nutrients).

Clay regulates various elements in the water (too much: they adsorb some, not enough: they release), enhances drainage...

Some species of bacteria needed for the vital nitrogen-cycle thrive inside clay.

That's the reason why clay balls/pebbles/pellets are omnipresent in many types of plant cultivation projects.

If you added the pottery fragments to the compost pile they would be “baked” again, albeit in a very different environment, and the finished product would have structural diversity closer to soil. Normally that would be rocks, but if your goal is to grow food clay rocks might be better for many reasons.

It could just be incidental, some broken pottery unintentionally mixed into fire ash that was intentionally spread on a field.

Just a wild guess here, but isn't all kinds of stuff usually added to soil to help regulate moisture and pH levels?

You're all overthinking it. They dumped their kitchen waste in the fields, and it happened to contain broken pottery too. It's the same for other archeological sites all over, many are waste dumps that contain interesting objects.

They probably couldn't be bothered to sort trash and compost into separate bins.