Mainly because their dietary needs can't be met in any tank... they can wipe out any and all of their food sorces super quickly... if they DO manage to stay alive in a larger aquarium you will have an instant tank bulldozer.. they will turn over everything without trying...
Most horseshoe crabs of the 4 species all reside in cooler water temps-not equal to the norm of our tropical reefs.... the temp alone can alter the behavior and change the lifespan of the crabs... in fact, 2/4 of the species are protected by law currently to prevent people from over harvesting them or bringing them into the hobby (they are also used to catch eels for the sushi trade). These guys aren't even really a true crab... they (like hermit crabs) are related to spiders, ticks, and all those creepy aracnids.
another fun fact-horseshoe crabs blood has copper in it naturally. They have hemocyanin instead of hemoglobin and if bit/cut open the blood can release the copper compound into your tank-taking out your inverts.... really thats the only complain I have with the horseshoe crabs info in the database, these guys won't be affected by copper because its a trace element in their bloodstream.... its ranges from about 50 to 70% a liter in their blood.
at the aquarium we try to not keep these guys at all because of how delicate they are- Even though we are a great functioning aquarium there are some things we believe are just better off left in the wild. These guys just aren't made for our home aquariums, they are not easy to take care of no matter what anyone says! lol.