Frank made a mistake? (spoiler)

Frank's soul is tormented throughout the film by the sights of horror, sadness, and despair in the streets of New York. He feels broken, believing he failed to save anyone for months, especially haunted by the death of a young girl named Rose, whom he failed to rescue. Frank describes New York streets in a pessimistic way, but contrary to what we might think, most characters in the film, despite the great suffering they experience, express a desire to live. Think about that..

* Noel seems happy when Frank tells him he can die in the hospital, but when he arrives at the hospital, he just runs away.
* The person who attempted suicide did not actually wants to commit suicide.
* Even babies that are not supposed to be born want to come into the world.
* Mary didn't kill herself despite her difficult life.

And there is one other person, Mary's father. He continued to fight to stay alive even though there was supposedly nothing left to fight for. Simple things like a piece of his favorite music made him wake up. In the hospital, he fought like a lion, and his condition improved against all odds.

On the other hand, he also begged Frank to kill him. I found it strange because his body said otherwise - he did everything to stay alive.

So my theory is that, due to his mental health, Frank didn't 'read' Mary's father's signs correctly. It is not only that he suffered from hallucinations, but he didn't understand Mary's father body Language. Mary's father actually wanted to keep living, even when connected to a ventilator 24/7. Still, Frank killed him to stop is suffering.

The narrative of the desire to live despite the suffering is woven throughout the film so that I see no other interpretation. Mary's father wanted to keep living.