I'm not one to argue with an active imagination so lets entertain this. So, despite the fact these are killing off reefs en masse and the population of things that predate on them isn't keeping up with theirs - all that stuff from Planet Earth and Blue planet (which may be a good source to learn more about these guys to see how much the eat) lets ponder keeping an animal like this as a thought experiment.
They are one of if not the largest starfish in the world, have ~15 arms give or take a few and are roughly 15" big.
Because of the size I would say any tank that is 12" wide is out of the question. you'll either need to go big where the starfish can move around lengthwise or if you go with a shorter tank you'll need one wide enough to still accommodate an animal that large.
According to wikipedia (not a primary source but a quick one for facts) they can live off of stored energy for up to 6 months when food supplies are low but can eat up to 6square meters of reef a year.
You'll be looking at a large tank, corals from its native habitats which are indo and pacific, and you would have to determine how much food it can live on. Does it need to be fed enough to just survive. Can it always partially reserve energy and live on that so you dont have to give it as much coral, or do you have to feed it excessively to keep those reserves built up?
Those are interesting questions indeed. Handling it and getting it in and out of the store and to your tank may provide a challenge as well, theoretically speaking.
Anyone else have thoughts on this? Definitely one of those things that should be left in the ocean but why not see if one could be kept captively for fun? I'm sure a large aquarium center (like the large one in san francisco, chicago, atlanta) would entertain having something like that on display. How sad it would be to feed it, would you aquaculture its food? Again, how do you know it has enough? Ok im really curious now!