I don't think it's broken in the sense that it's too good and just dominates everything, with no way to counter it; there are several ways to counter it, in fact. Hard counters, too.
I do, however, genuinely believe that the Wk is too cheap. There is no entry or combination of entries elsewhere in the codex for the same cost that can match a WK.
Personally, I'm against using gargantuans and super-heavies in normal 40K games. I've stopped using my WK for these reasons.
Another terrible side-effect of introducing gargantuans and super-heavies to normal 40k games is the inclusion of destroyer weapons. Suddenly, good old-fashioned MCs and tanks are utterly obsolete. A tank is supposed to be somewhat durable - what's why you spend the points on one, but a destroyer weapon laughs at that armor.
No, remove gargantuans and super-heavies, as well as destroyer weapons and I'll be happy. We're sort of house ruling them out of our games anyway, me and my buddies.
So to summarize - there are several ways to counter a WK. That's not the issue. If you want to kill it, you can, just not with lascannons or multi-meltas.
What I think is wrong with it is that it's too cheap given its versatility and outstanding performance, in relation to the rest of the codex entries.
Furthermore, it goes against the traditional Eldar playstyle of specialization: our units are tailored to a specific task. If you use them the way they are designed, you'll see fantastic performance. If you use them sub-optimally, you will notice a terrible performance. This is the opposite of a Space marine army, for instance, where each unit is pretty strong and will perform most any role well enough. The WK is exceptionally good at EVERYTHING. No, I don't like it.