>>149365623
>it was made very clear that Doomsday would have killed him and everyone around him of
Clark told Rudy "that's enough" because he was scared doomsday was gonna kill rudy, which he did. The "very clear part" was the draining let them inject the downed doomsday to keep him asleep. It was also "very clear" that superman getting angry at rudy's death made him stronger and he was trashing doomsday so bad people had to pull him off. Time Trapper doomsday later admits superman wants to damage him minimally so that he doesn't adapt as strong. Which supports the interpretation that parasite's draining was just for the dream serum and superman getting angry is what actually put him down. In fact, the fight was planned by Time Trapper doomsday to give him the last adaption to overcome the Prescence which would encourage superman to hold back (again, until Rudy's death).
Lastly, even if we take your interpretation as totally true and the full story, as >>149365636
points out, this king of hell doomsday that scared the first of the fallen enough to loan his warn on heaven suit to supergirl was only able to bruise superman before rudy showed up.