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I have read various arguments that a single Kryptonian superhero is capable of ending all criminal activity on Earth in a very short space of time. Some of the proponents of those arguments go further and claim that Kryptonian superheroes like Superman and Supergirl 'allow' all manner of human suffering in Gotham and Star City due to them 'respecting' Badass Normal heroes like Green Arrow and Batman, and accordingly staying uninvolved.
I disagree with these arguments, on the grounds that I can see a number of practical limitations that would prevent this from being feasible. (I will use Supergirl as an example, but everything applies to Superman, Power Girl, Superboy, and other Kryptonian or half-Kryptonian heroes as well.)
1) First of all, no matter how fast Kara is, she can only be in one place at a time.
2) Kara's senses might be superhuman, but they have to have limits. If they were completely unlimited, then she would only be limited by the vacuum of space beyond the Earth's atmosphere, and accordingly she would hear every single thing on the planet, underwater, and in the air all at the same time. ...this alone would give Kara a terrible headache, possibly bad enough to render her comatose. The same goes for her other senses.
3) Kara can only do something about crimes that she is aware of. The limits of her senses come into play; she can gather more information from the news media and possibly the authorities (depending on the exact nature of her professional relationship with them) but they have limits as well; and then there is the temporal distribution of criminal activity to consider – because not every crook is obliging enough to commit all of their crimes in a very short space of time.
4) It isn't enough for Kara to 'catch the bad guy' – she needs to find evidence which can prove that they are guilty of at least some of their crimes. Yes, her powers give her some advantages in these endeavours, but they don't solve all of her problems – especially problems like all of the evidence having been meticulously gathered and destroyed by the perp(s) while committing the crime(s) in question, if such a turn of events should come to pass.
5) Just like any human law enforcement official, Kara needs to sleep, eat, and attend to her personal grooming and hygiene at some point. She also needs downtime every so often to keep from losing perspective: she needs to maintain a healthy work-life balance. And then there's the problem of her 'solar flaring' and blowing out her powers: if that happens, then she's down to human levels and limitations of physical capability.
...the bottom line is that Kryptonians are physically very powerful – but they are far from omnipotent and omniscient and unstoppable. They have limits, and therefore they can only accomplish so much. Their powers provide them with advantages and improve their ability to survive dangerous situations – but that's all.