The big problem is not how many American troops would die in a conflict with North Korea (such a conflict could be "won" with zero American losses, in theory), but how many South Korean and North Korean civilians would die. Unfortunately, nobody has figured out a way to remove the North Korean regime that doesn't result in hundreds of thousands of South Korean civilian deaths.
1) overestimate the number of such planes the US has at it's immediate disposal
2) overestimate the effectiveness of artillery triangulating systems
3) underestimate the shear size of the DPRK forces
4) overestimate the amount of time each artillery position would have to be active to kill thousands of civilians in a densely populated metropolis.
And finally: fail to take into account that if you've had this idea, chances are people who do military planning for a living have probably thought long and hard about it as well.
The only way to guarantee taking out all of the Northern artillery positions would be carpet bombing with nukes, which would result in lots of deaths in South Korea from fallout (not to mention all the other much more serious problems involved, such as establishing a precedent of preemptive nuclear attack).
In reality, the situation is even more complicated than this simplistic analysis. It's not so easy to take out an artillery position in a previously undetermined location, especially if that artillery position can be hidden in a cave/bunker on a moment's notice. More so if there are thousands of artillery positions spread over many square miles.
Even if the artillery in the North survives only a few hours or even a few minutes the sheer number of them and the population density of the regions of South Korea within artillery range would lead to catastrophic civilian deaths in the South.
The South Koreans have been militarily capable of stomping all over the North for decades, without American help. The fact that they haven't yet, despite numerous provocations from the North, is a testament to the huge losses that they would inevitably face if a hot war broke out again on the Korean peninsula.
Edit: Current estimates are that North Korea has the capability to fire around 10,000 rounds a minute into heavily populated regions near Seoul.