So it's pretty clear that these doors are an effective means of handling lines when the distance to the deck is too great to accommodate that activity. That was always my impression of them. A few commenters who seem to know what they are talking about here also mentioned watching the anchor rode come up from the platform. Is there a reason this cannot be accomplished with a camera leading to a display at the helm station? It seems like such a system would be more effective than a crewman with a radio and trivially inexpensive compared to the cost of installing the door. I would imagine that you'd have to worry about salt spray on the lens, but am I missing something else?
You would need the camera where the anchor is deployed on deck, not at the helm. On megayachts, one cannot launch the anchor from the helm. The brake has to be manually loosened at the anchor. So there is usually always someone on a radio telling the captain how to maneuver as they're anchoring.
I am yet to see a camera that is able to turn a twisted anchor or get lines, other chains etc off it if they are caught. On larger systems in addition to the brake there is also a guillotine and devils claw on the chain, these all have to be released and applied manually. Someone needs to be in attendance when operating the equipment for both dropping and raising as the loads on it are very large as is the equipment and damages can easily be done to the vessel and its equipment both dropping and retrieving the gear if the operator is not on top of his/her game.