If some banks are thought to be too big to fail, then, in the words of a distinguished American economist, they are too big. It is not sensible to allow large banks to combine high street retail banking with risky investment banking or funding strategies, and then provide an implicit state guarantee against failure. Something must give. Either those guarantees to retail depositors should be limited to banks that make a narrower range of investments, or banks which pose greater risks to taxpayers and the economy in the event of failure should face higher capital requirements, or we must develop resolution powers such that large and complex financial institutions can be wound down in an orderly manner. Or, perhaps, an element of all three. Privately owned and managed institutions that are too big to fail sit oddly with a market economy.
The discussion of whether it's a good idea to combine retail banking and investment banking seems to muddle the point a bit, as you can in principle have an enormous balance sheet without combining the two. And there's no real indication that King is willing to make overgrown banks smaller. (Higher capital requirments make a big bank less likely to fail and constrain balance-sheet growth, but they don't force banks to shrink, nor do they make failure less dangerous if it comes to that. Resolution authority should make failure less dangerous, but that assumes it can be executed in a timely manner, which gets more difficult the larger the institution.)
Still, it's not nothing when a leading central banker stands up and proclaims this.
Update: Actually, the more I think about this, the more I think King was on the right track with his concerns about retail and investment banking combinations (i.e., what came after Glass-Steagall fell apart). The issue isn't size per se--the failure of an enormous but plain-vanilla commercial bank wouldn't be that scary. It's size plus complexity that gives you cold sweats. Which is to say, complexity is tricky enough to deal with on a manageable scale. But when you have an enormous balance sheet that's also really complicated, it's not clear you could unwind it quickly enough even if you had the authority.