On the contrary, Fiddles is not limited by the "interrupt".
He really is. His ult is nice and all, but if it's on cooldown, something like 80% of his damage output comes off of Drain, which is a very slow channeled spell. Interrupt that and suddenly Fiddles is doing no damage at all until its cooldown comes back up. His E (the silence) does fair damage but has a VERY long cooldown for a damage spell, Q doesn't do any damage at all, so the only consistent source of damage he has is Drain. Anyone who can interrupt him consistently has no fear of Fiddlesticks.
In other words, pick TF and yellow card anytime he starts to drain. Voila, Fiddles is now harmless.
As for his ult, yes, it has nice numbers on paper. However, your whole "this damage kills an AD carry" statement seems to disregard the fact that the carry in question probably just isn't standing there eating the damage and doing nothing in response (and apparently has no MR). Unless he's also feared that carry, they're probably shooting something, and by the time Fiddles has a level 3 ult a good carry probably has a fair amount of lifesteal. I have watched Vayne sustain herself through an entire Fiddles ult just by carrying on through the teamfight killing people and healing through it. Would that have happened if the team had focused her like they should have? No, of course not, but she wasn't instantly killed just by being in an ult that does enough total damage to have killed her, either.
Why not? Because that ult doesn't do all its damage up front.
It's like marveling at the massive damage Nunu's ult is capable of doing. Yeah, he can legitimately one-shot carries with it if he builds heavy AP...but how likely is he to actually pull that off, even with his massive slow on Q to try to keep someone in it? Not very, not unless no one sees him doing it and/or no one can interrupt him/flash away.
Fiddles is the same way. Unless you set things up perfectly for it (ie: jump into the middle of an ongoing teamfight when everyone's already engaged and has blown some of their best burst spells so they can't just insta-gib you the moment you appear in the middle of them), your ult is going to do a fair amount of damage, but it's unlikely to just kill people because they started out near him. This is especially true if you pop Zhonya's, since it only takes a second to run away from a stationary Fiddlesticks and be out of range of the storm. You have to chase people if you want to really maximize the ult's damage, and if you're chasing them, they can kill you (and since you can't drain while you're chasing, you can't really stop them from killing you, since you're very, very squishy).
Fiddles can be lethal. He's an absolute monster when it comes to disrupting teamfights and forcing people to scatter, enabling his team to pick off separated opponents or get to those VIP targets they might have otherwise had trouble reaching. He's pretty good at dueling anyone that can't constantly interrupt him once he hits that magic level of AP/Vamp that turns his Drain into an "I don't give a fuck" button and his CC in a teamfight is pretty boss.
What he lacks: durability, consistent dps/teamfight damage and, most importantly, mobility
. Fiddles is almost as easy to avoid as Mordekaiser in terms of his ability to chase. Maybe even easier once Morde gets Rylai's, since Morde can just spam E to gradually catch up with someone and Fiddles doesn't have any ability that spammable (since Drain, his only low-cooldown source of damage, requires him to stop moving to cast it). Ahri got nerfed for having great damage, great control and great mobility even when she built semi-tanky due to the combination of her true damage mechanic, spell vamp passive and her triple-dash ult. If you build Fiddles even a little tanky outside of AP items (Abyssal, Rylai's, Zhonya's, etc.) his damage is sub-par and he has zero mobility beyond his long-cooldown ult's channeled Flash, which is too slow to be used for chasing and too easily interrupted (and on far too long a cooldown) to use for escape.
tl;dr - Fiddlesticks is much better at enabling his team to get kills than he is at executing people personally. I like to think of him as an offensive support more than an AP carry.