I know it's cliche, but it is the better of several bad solutions. The only alternative is that we wait and hope the regime falls in on itself, but do we really think this will happen still?
So yes, it will likely be very bad for Japan and South Korea, but I truly feel sorry for those countries if they think their future gets any rosier a decade or two down this current path. I have some pretty bad news for some people who have been hiding under a rock for the last 60-70 years: North Korea's plan is to re-unify their peninsula. And they are not very happy about what Japan has done to them in the past, either (they literally call Japanese "Jap bastards" in official literature, not simply "Japanese"). Make no mistake, if North Korea ends up with the ability to strike with ICBMs or to have subs idle off our coasts, we're gonna go ahead and sit that one out-- they can have South Korea. That's what is truly frustrating.
An alternative path is that Japan and South Korea get nuclear as well. I'm sure China will be pretty happy about that one. Sigh.
I'm looking at this through the perspective of 25-50 years down the road, unless we want this to be a complete gas can for our children, we have the responsibility to nip it in the painful bud now.