Replying to your Plot Twist point:
When Myeol Mang was idle, it caused a lot of chaos in the world of the living. What would happen if he died/disappeared? It would break the balance between life and death. He is also powerless against God as we see in recent episodes. His only role and power are to maintain the balance.
Since he can't end the world on his own, that's where Dong Kyung's wish comes in. A human's wish to cause destruction and end the world is exactly what Myeol Mang is looking for. Myeol Mang is able to grant the selfish wishes of humans once in a while. He is unable to end the world for himself (our selfless diety) but he can fulfill a human's wish.
With the end of the world, the deities would cease to exist. There would be no 'garden' and hence no 'flowers' or 'gardener' or the 'butterfly'.
The deities solely exist for the living. it's similar to the theory of how Gods exist because they are remembered by humans and prayed to. They would disappear if forgotten. So yeah, Myeol Mang can't kill himself or experience death but he can use Dong Kyung as the trigger to make his existence itself useless by bringing an end to the world, and essentially disappear for good.
That's just my take on this! However, the Goddess is so unnerving. I wonder how easy it would be to understand her if she stopped speaking so poetically, and also stop manipulating MM. The dude is confused as hell.
What I am very curious about is how did the goddess, Doom's "mother" die. I get that the reason the girl in the hospital is always sick is that she has to maintain the so-called 'balance' of life and death. Hence, she suffers while she creates. And when she died, why did Myel Mang sob like that? Was that his first time experiencing her death? If not, then does he not know that they will be born again? Or was he crying for the diety that died then? Does that mean every time the deity is reborn, it's a different personality, not the same one? then would that mean Myeol Mang isn't the first Doom deity? So even if he dies, he will respawn but not our Kim Saram but just someone else, that takes on his role. And if that is the case then it makes sense why the Goddess doesn't want the world to come to an end just because Myeol Mang wants to die. Because it is Myeol Mang now, tomorrow a replacement will come in his place, but no idea when that tomorrow is.