I never used this trap door. Presumably, it's to dispose of ash on a regular basis. Is there any particular reason that using this is a bad idea? There's a door/ access panel in the basement to clean out the accumulated ash, which makes me wonder what the benefit is of using this. I can just fill a bucket and carry ash away every fer fires.
The benefit is that (with the door below closed as per normal practice) you don't need to wait for anything to cool (it's going into a nice masonry chamber, nothing to burn) and you don't need to carry ash through the house. You dump the ash (hot or cold) down the hole all winter, and when spring comes you shovel it out from the basement and go spread it on your garden (unless you are in an alkali soil area. In acidic soil areas wood ash is quite beneficial to gardens.)
@jstola's nightmare scenario is frankly a bit far-fetched. Those cast iron doors don't just fall open by themselves, and any smoldering combustion byproducts would be filtering up by the trapdoor, into the chimney, and out of the house.