On the other hand, if North Korea wished to strike back, it could wreak its own brand of havoc.
And the timing of the attack is an issue, diplomatically. Strike before a test and many would consider it a provocation by the US. strike after, and north Korea has nuclear weapons (potential, at least).
And North Korea is a far harder nut to crack than Syria or Iraq for this sort of deep penetration strike. Not sure what the odds would be on the strike, as North korea has generally obsolete air defenses, but lots of them, and to a certain extent their aerial strategy is oriented around air defense. Penetration without detection would probably be difficult without stealth aircraft (the radars could easily be defeated, but their number makes total suprise tough), and while the North Korean air force may have trouble making a decent intercept, the sheer volume of ground based fire will be dangerous, to say the least.
There is an even bigger issue then that militarily. If the United States upsets Dear Leader's nuclear ambitions, then we can garuntee that the Nork's will use ever bit of artillery they have to level Seoul from behind the DMZ. Not to mention large numbers of conventional and chemical-tipped ballistic missiles landing further into South Korea and Japan.
One would have to be able to take out all of North Korea's long-range artillery pieces within hours. Given that North Korea has some 6,000 artillery pieces, and undoubtly a large number of them are aligned along the DMZ, such a feat would require a substantial number of aircraft... which would be absolutely impossible to hide from either South Korea, Japan,
and North Korea. None of whom would approve of this kind of attack.
The ballistic missiles would be even harder to hit, the North Koreans have ballistic missile that is almost certainly in excess of 900 usable missiles. The majority of these (over 580) are Hwasong-5 and Hwasong-6 missiles, capable of hitting all of South Korea and ~200 Nodong-1 missiles which can reach all the way to southern Honshu and an unknown quantity of Nodong-2's and BM25's, both of whom can target all of Japan and the latter of which posses MRV's (Multiple Re-Entry Vehicles, think a MIRV except none of the warheads are guided during the re-entry phase).
All of the missiles I have listed above can be launched by road-mobile launchers, and given the success we have had against road mobile launchers when fighting Iraq in both the Gulf War and Iraqi Freedom we would be better off trying to shoot those things down
after they launched.
The cost to a surgical strike against North Korean nuclear sites would
way, way, outweigh the benefits. It would be a disaster of monumental proportions.