I'm not sure I'd entirely agree. It would be another thing if the Eyrie could be infiltrated or besieged into submission, but since I understand that it's also got a warm-water port on the other side of the mountain from the only road of access, it seems to me that you need both a much badder army and a much badder navy to take on the Vale. Mind you, the Vale lords besieged it with no problem in the latest book/season, but if I recall correctly that's only because one of them (Duskwood?) also controlled the seaport.
Sure, it's a whole bunch of inconvenience to maintain... but arguably less inconvenient than going to war, or having your castle sacked, every now and then. So far in the War of Five Kings, the death toll has been minimal in the Vale and devastating everywhere else, mostly thanks to the build and strategic location of the Eyrie. My only other concern regarding the castle would be: How many peasants can it hold? If you can't shelter your subjects there, then I'd have to agree that a castle like that just isn't worth it. Army comes in by sea or land that's stronger than yours, you run back to your unassailable castle, they slaughter all your townsfolk... well congrats, you lose. Enjoy your next couple generations of financial decline and civil unrest, due to not having any people around to make money for you anymore (and/or being generally pissed off at you for what happened to the others).