Chamotte with clay binder is the basis for almost all cheap refractory products. What do you want more? You can try using it as a cat litter or flower substrate, but sintered at 1400°C ceramic grog has too low porosity and is too expensive for such applications.
You can give power to ritual objects. For examples certain ceramic drums and vessel flutes used in religious or ritual ceremonies might be well known to have certain powers. One can spread this power by breaking the instruments into pieces and use it as grog for the production of ten new instruments. These instrument are now insoul with the power of the original instrument. So this way religious authority and leadership can spread their influence by having a few more extra pieces of powerful instruments and these can be distributed to other temples in other cities that they control or as gifts to other polity as a sign of friendship and alliances. We find these in ceramic Maya musical instruments. These is no reason to use grog but they do anyway.
Not sure if the above is what you are asking for or if you were just trying to get technical functions in terms of ceramic production. I hope it helps.