"Isn't strong by any means" -- yet I can burst down just about anyone at 6, and I can kill someone in lane within the first 5 minutes with a few well-placed poke combos. After that? Well, let's just say that squishies should be afraid of every wall and spot they don't have warded. ^^
The low damage on his moves is offset by his incredible mobility and the low CDs on things (relative to other mages and assassins). The mana cost becomes irrelevant as soon as you build a Catalyst (so long as you don't just spam his R), so that's not an excuse either.
You know why people run from LB and Fizz? It's because they are braindead champs who can just mash keys and instantly kill you. They don't take any effort, so anyone can come along and do incredibly with them (my first game with LB, I was 19/1. First with Fizz, 18/6). Kassadin is different; he takes knowledge of both his kit and his target's, and has to do everything right, or lose. Not many people can play Kass to his full potential, sort of like Azir, so no one is afraid of a Kass. When you go 24/1 though, it's always satisfying to see Kass banned in the next match. :P
And, yes, his W adds the damage of Lichbane, Luden's, Statik, Hydra and all that as well, so it would be really broken for it to have a really high base damage.
So, please, don't try to tell me he's not strong. He's just not (for lack of a better word) noob-friendly, same with Azir (though they're making Azir into yet another braindead thing, so, so much for that). If you sit down and learn his kit really well, learn what he's capable of, know what your enemy is capable of, and how to exploit their weaknesses, then you win. Kass is the real master tactician, not Swain. :P