I’ve never seen such a small flame, I think they can’t exist. Why? I don’t know.

Your intuition is correct and it’s quite simple really. A small fire cools down faster than it can keep/generate its own heat.

Surface area of the fire (which correlates with how quickly it cools) grows with the square of the size of the fire. Meanwhile volume of the fire (which correlates to how much heat it generates, how much fuel it is burning) grows with the cube.

At small sizes, the surface area can win out against the volume. However, because it grows with the cube, the volume eventually wins as the fire gets bigger. So a fire can only get so small.