On the topic of saving people, I will namely pinpoint certain situations where the tactic of preventing one’s death (which will simply be abbreviated as POD) is appropriate or not.
I’ll start of with Shinichi’s attempt during the end of the Moonlight Sonata case (File 67.13 – 67.17). In this scenario, POD would be appropriate. Although Asai Narumi killed at most 3 men to avenge her father’s death, Shinichi willingly tried to talk her out of suicide, but to no avail. His attempt, however, is agreeable if we consider the morality of justice being served; in this case, committing suicide would be the “easy way out” for Narumi and thus, would not atone for her crimes (like being sent to jail would). Therefore, Shinichi kept that in mind, and although he ultimately failed (which in turn scarred him for life), his act of POD was not selfish in any way because he was given the opportunity to save Narumi’s life and primarily focused on saving her life. However, he cornered her in a way that averted him from doing so. Such cornering a suspect would indeed be selfish had he not made an effort of POD, which leads me to the next case.
When Shinichi prevented the murderer from committing suicide during the Distinguished Family's Consecutive Accidental Death case (File 153.13 – 153.16), POD would again be appropriate. After realizing his mistake during the Moonlight Sonata case, Shinichi saw ahead of time the killer’s future endeavors and successfully prevented her from pursuing suicide. Once again, he was given the opportunity of POD, and despite the fact that the person was a murderer, Shinichi saved her life not for the selfish reasons of being a hero, but for serving justice (which is essentially the reoccurring theme of Detective Conan).
Now for a more controversial example of POD – when Shinichi and Ran saved a serial killer during the end of the New York or Golden Apple case (File 354.8 – 354.14). I’m 50/50 on this one. For one scenario, letting the serial killer fall to his death would not only make it easier for the police to capture him, but would also save lives down the road, let alone Shinichi and Ran’s lives, had the serial killer managed to escape. For the other scenario, saving his life would allow him to serve justice suitably if he was subsequently captured and would possibly change him for the better (as cheesy as it sounds). But considering the fact that Shuichi Akai said, “Every crossing to this street is secured already” when he decided to leave Ran alone, I think it’s fair to believe Ran and Shinichi did the right thing since there would be nowhere else for the killer to escape to. Technically, it wasn’t Shinichi and Ran’s responsibility to let him die; one could counter this by saying it wasn’t their responsibility to save him either, but saving his life would allow higher-ranked officials to determine the serial killer’s fate after his capture. Who knows? Maybe the police department needed him alive for questioning, or maybe he would’ve been sentenced to death anyways, so it could go either way. But because it’s the police department’s responsibility to determine the killer’s fate, not Ran’s nor Shinichi’s, I would say POD is appropriate to a degree. This is probably the only example I can think of when I actually question Ran and Shinichi’s motive, but I don’t think their intentions are anything immoral.
Lastly, when Ran practically sacrificed her life to save Haibara during the end of the Halloween Party case (File 434.6 – 434.9), POD would definitely be appropriate because Ran’s main focus was to protect Haibara whom she believed was still a child. Even if it meant her death, Ran still jumped in front of Haibara and caught Vermouth off guard. There’s not much to say in this scenario since it evidently demonstrates Ran’s selflessness.
In the end, I DO NOT believe that Ran and Shinichi are arrogant for trying to save lives. On the other hand, I DO believe it is selfish to THINK that you can save everyone's life in any circumstance. It's pretty easy to assume that these two have this thought process in mind, but I honestly believe it is the other way around - they KNOW they CAN'T save everyone's life. But it wouldn't be wrong to try to save as much people as they can when given the opportunity to, and so far, every POD example I could think of in the DC series has a legitimate reason behind it; most of which are associated with serving justice. The closest (and probably only) example of when POD is not appropriate is during the New York case when Ran saved the serial killer/Vermouth from falling, but like I said, the killing spree would have ended regardless if she saved him or not because the surrounding streets had been secured by law enforcement. Overall, the ACT of saving everyone is far different from the THOUGHT of being able to save everyone. I apologize for such a long post, but I just wanted to get my point across.