mmmm..... the problem with this story is that a vigilante may not have the complete facts or correct identification. He might target the wrong person out of mistaken identity or false accusations.
In this chapter, he says he chooses criminals based on previous convictions, who continue to repeat their offenses after release from prison. But he won't know whether they continue a life of crime unless the person admits it himself directly in front of him. The criminal in the first chapter clearly committed assault on the bus driver in front of the MC. But in the 2nd chapter, the MC attacked the target before verifying whether the target was still committing crimes. A doctor would reasonably have syringes in his backpack. So seeing the syringes (after hitting him) doesn't really prove anything. Of course, the author shows us the panels where the target appears to be preparing to commit a crime, but the MC did not personally observe this.
You can find real life stories in the news about how innocent people are killed by vigilantes based on false accusations. Innocent people accused of being drug dealers, gang members, informants, spies, etc. The vigilantes who killed innocent people get away without punishment, so they become like the criminals who they execute. But in real life, I would think most vigilantes are fairly violent people who don't really have as much of a conviction for justice than they claim.
So I would predict that this Manhwa will develop an arc where the MC kills an innocent man and has to decide how to deal with the consequences.