Honestly I had the same mindset as you. But then again....I think he doesn't want to kill the old guy just yet because it's not time yet. Maybe he's patiently waiting when the time is right. You know to take over the company right under the old man's nose. So that's why Sangmin can't kill the oldman yet. Because if he did...It would kinda ruin his plans. I'm guessing he wants to ruin the old man's reputation as well.
Cause they have competition for that hospital (their relatives), currently the Dad (mean old dude) is the head, but since the blonde dude hasn't solidified his position yet as successor, he might lose it if his dad dies to one of the relatives. Currently, his strongest ally is the dad (eventhough he's a jackass). He has more worth alive than dead....for now.
Question:
Why doesn't blonde guy (sorry, forgot his name) kill old dude? We know he has no problem with killing. Kill the source of the problem. Kill the real villain. JiHyun won't be a problem so long as ugly old man is dead.