The challenge would be stability, as the expansion and contraction due to heat would be significant. Would clay be stable
enough if it wasn't kept absolutely pure and then fired in a kiln? What you are suggesting is akin to a
cob oven. My concern is that if it cracks, you'd have a danger of a
carbon monoxide leak. Very dangerous.
But if it were professionally made and fired, like a kamado grill/Big Green Egg, it would be very stable and able to withstand the tremendous temperature extremes. I'm waiting for the day when someone manufactures these professionally out of clay (again, glazed and fired like a Big Green Egg), with a tight gasket at the bottom that seals perfectly.
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf