So... no one at the hospital noticed the relatively fresh wounds on his arm that suggest he hurt himself and might be suicidal, so even if they run some tests, they still shouldn't discharge him just like that?
I think it depends on the country, then. Where I live, if injuries like these are noticed, the patient undergoes a psychiatric evaluation. If it turns out that they actually intend to end their life (in this case, he was hit by a car, so the question is whether Mokyeon will tell them that, or lie about how he got injured for Nanjo's sake. Since he walked in front of a car while drunk → he could have done it intentionally, especially considering the injuries on his arms), then here we have the option of emergency psychiatric treatment, even without the patient’s consent, provided that the conditions set out by law are met. That said, obviously, I don’t necessarily expect a fictional story to be absolutely accurate in every respect.
Okay, like, seriously, I don't want to be a hater or anything, but... so basically... it was such an obvious cash-grab season, especially because even if we didn't have a problem with the "plot" itself, it was so poorly written, omg. Things just magically got solved in, what, 2 chapters? XDD Was it really worth doing it like that?