Edit: Hmm. You lot make some good points about just how many 'small' hits they could pull off, assuming that each gun emplacement has ammo etc. so I did a bit more research. Seoul Capital Area has an area of ~11,000 kilometers square[0]. Assume a generous affected blast area of roughly a hectare per shell (we're talking about shelling a population center here so you don't have to level every building to have a serious impact) and that's 1.1 million shells (if they're firing with uniform distribution, which they won't be) to seriously damage the city. Assuming a normal distribution where they all aim haphazardly for the CBD and let fly, it's even worse, call it 500k shells at a guess.
10k emplacements, if they have 50 shells each, will deliver this in (as per post below) 8.3 minutes. So yeah, even if it can't "pound Seoul into rubble" it would be a highly undesirable outcome for the South Korean people.
I take it back. Conventional artillery isn't slow if you have enough of it.