11 liveaboards and counting and none have "allowed" footwear on board. They are usually stored for you upon embarkation and given back to you upon disembarkation though I am sure there might be exceptions and is not a rule. I think someone was able to wear flip flops due to some medical issue but they were given very specific instructions on safety and having to maintain hold of something at all times while wearing them, especially while in motion, but I think that is probably sage advice for everyone regardless.
I kind of like the organizer idea as some are really light and easy to pack. I don't know that I would actually bring one but I can see the convenience of this, especially not having to dig in what they call a "closet" or "wardrobe" for something that you frequently might want to access easily. Thinking back on all the cabin doors and them not being standard size along with the clearance between the threshold and the door itself, I wonder if it actually fits well enough (in length) and that the door shuts securely without issue or damage to the threshold or door.