Well, yes, if you aren't using them in their best capacity, they won't look overpowered. First off, you can station them in Forts, which effectively bypasses the "4 per city" limitation. Second, they can attack cities, which is where they quickly show their overpowered nature. By softening up the defenders before an attack, you can virtually guaruntee that you won't lose any units. I've done a march through enemy territory and not lost a single unit, thanks to Airships doing a number on the defenders pre-attack.
Concentrating them with forts is a logistical pain in the bum, and more difficult as you push deeper into enemy territory. But I still don't see it as really a problem, since a concentration of airships is a hell of a lot of resources that weren't spent building the boots on the ground to really capitalise on the advantage they give. I find they're best in modest numbers - denting the really tough nuts so that you don't have to waste sacrificial units or flanking cavalry on them, then hitting them with siege with the better odds; or for hurting lonesone targets of opportunity in the field so that cavalry can easily pick them off.
If you have military superiority anyway, sure, airships are a great way to build, maintain and project that extra strength, but in a face-off between two roughly equal armies, one airship-heavy, one airship-light but with more grunts, I'd put my money on the airship-light army every time.
And finally, your comment about a stack with medics being able to "shrug them off" doesn't make any sense - if you are using Airships to soften a stack, then that stack is almost certainly either (a) mobile, and therefore not able to heal, or (b) about to be attacked by you, and therefore not able to heal. If you are using them to attack stationary units that you don't plan on attacking, of course they won't be overpowered. But under those circumstances, a Stealth Bomber wouldn't look overpowered attacking Axemen.
Sure, but any attacking stack is going to be hounded by masses of the AI's suicidal artillery anyway before it gets to its target, which concentrate damage much better than airships do, even if they mostly die in the process. But airships are each only doing ~10-20% damage per turn to a single unit, which really isn't a lot to a big SOD. Unless the airships massively outnumber the units in the stack, it's not enough to easily pick them off in the field, and it's not enough to really stop them being effective against artillery-(or airship-) weakened defenders, particularly en masse, and particularly if you left some promos spare. And with a good healer, you can even heal most of that up on the turn or two it takes the artillery to bring the defences down. Otherwise a bit of quick recouping in the newly-captured city will still get them fit and happy again.
I've never found the AI's hordes of airships to be anything more than a nuisance, and I've put my faith in my own fleet of defensive airships before, but when Genghis sends his massive stack over your borders, they're really not going to slow his stride.