Thinking on it for a moment, I think the small hole size on the mesh doesn't clog because the grain size of substrate is often significantly larger. The irregular size of the substrate particles prevent them from sealing against the fibers of the mesh. Yet it still allows ample drainage BECAUSE of the large holes in the pot. The mesh, aided by the aforementioned properties of water, drains across its entire surface as water wicks from the outer fibers the ones in the center, but only the area congruent with the hole.
Edit: Re-read, and the relationship between the large holes and the mesh wasn't made clear.
If there was just a large hole, no mesh, then the water would run out at the edges of the hole, the rest of the area being unnecessary. With mesh, however, the water will drain out slower. We've effectively reduced the hole size.
In conjunction, the mesh can only drain over the area of the hole, but effectively reduces size of the hole by say 50% (for the sake of example), therefore a larger hole is needed. Even so, the mesh aids in drainage by wicking the water via capillary action and surface tension across its entire area, draining as effectively as if the hole had been reduced by only 25% (again, just a number for the sake of example).