The torque a spinning block exerts on itself is smaller than it should be even after you take into account the fact that the moment of inertia of a block is larger by a factor of 2.
When you spin a block about neither the largest eigenvector nor the smallest eigenvector of the moment of inertia, the block will torque itself.
The torque is very small. This torque might be computed for a “Hollow Block” instead of a solid block, as noted here: Blocks Moment of Inertia is Wrong