I still don't understand this argument (or why we are having this discussion at all). Of course the trade is not to blame for the decline of these species, nobody is saying that it is. But the fact of the matter remains that, yes, they are in trouble. Be it climate change, ocean acidification, dynamite fishing, coral bleaching, a suit of diseases, they are declining at an alarming rate, and you still want to keep collecting these already threatened species for the aquarium trade? Why? There are more than 400 species of coral, banning the 66 that are most in trouble from the trade would still leave 344 available, is that not enough? Why?
Let me give you a clear analogy here as for why this line of reasoning does not work. Bengal tigers are nearly extinct. Pet trade has not once been mentioned as a reason for tiger population decline. Should we allow for tigers to be collected and traded as pets then?
Here's where your analogy falls flat on its face: Bengal Tigers number about 2000 in the world. We know a fair amount about them, including the population density needed to replenish the population along with the root causes of the population decline.
We have no hard numbers on any of the populations listed (most estimates I have seen for Euphyllia sp. put it in the millions.) We don't know the true root cause for the populations decline. No evidence is provided that preventing the very light amount of harvesting that goes on for the aquarium trade will have any impact upon the decline of the worlds reefs. The NOAA is taking a gun, pointing it in a random direction, pulling the trigger hoping some good come out of this.
If they were truly doing their homework, they'd be monitoring the Philippine reefs where harvesting for the trade has been banned for almost a decade now and see if there has been a noticeable increase in the health of those reefs. But they're either to lazy do to that (which is quite possible, after all they are .gov employees) or that data does not exist. If that data, or similar data, does exist and was presented as part of the NOAA's findings, I'd have no issues with this. I do have issues with people shooting guns in random directions though.