You do realize this is the same nation that just created a fifth-generation fighter something only Russia, China, and the US have done. Also, the K2 tank is likely the second or third best-produced tank in the world.
There's no clear definition of what a fifth generation fighter is, particularly since we have very little publicly available information about the performance of Russia or China's fifth generation fighters, but the KF-21 is probably in a kind of 4.5 category.
I'm also not really sure what military purpose creating a domestic fifth generation fighter serves other than showing off. These things are massive, massive resource sinks to develop and build, they're literally beyond human capabilities to design and, as Russia is demonstrating, being able to design one doesn't mean you're able to afford to build them in sufficient numbers to make any real difference.
But I do think you're correct in that it's very likely that the south would win in some kind of straight up military engagement. The problem is the cost of doing so, in lives and dollars, would be astronomical. North Korea has
a lot of crappy old cold war era artillery, and while the accuracy of those pieces might be a bit questionable, it doesn't need to be accurate if the target is cities. South Korea is a small country with a very dense, urbanized population. A lot of people live within range of Northern artillery pieces, and for every one of those people you kill or injure or whose house or workplace you destroy, there is a societal burden to be paid.
And that's not even factoring in the real strategic deterrant. It's not just the nukes, the north definately has chemical and biological weapons (it tests them on its own people). Fire a few shells full of nerve agents into the middle of Seoul (which some artillery pieces could reach) and that's a big societal burden to pay. That whole section of the city has to be evacuated and decontaminated, hospitals are overwhelmed, supplies of certain drugs run low, medical workers have to watch people die horrible and agonizing deaths, they suffer trauma and breakdown. Again, there's a cascade effect.
And meanwhile, what does the south gain? North Korea is incredibly poor, its population basically all have military training and many will be genuinely fanatical. Even if it doesn't turn into a terrible, long, costly counter-insurgency operation, that population is also unlikely to be able to adapt well enough to become economically productive for decades.
So now you're left with the task of developing the north and gaining the trust of its people while also having to repair the catastrophic economic damage inflicted on the south.
And this is assuming the nukes don't come out. If they do then this is no longer simply an economic burden, it's a global humanitarian crisis.