He doesn't deal with other heroes' problems because it's not in his character to do so. What I mean by that is Clark has his own life to live. While he could potentially become a god on Earth, he chooses to live a pretty average lifestyle by working as a reporter and pursuing a relationship with those such as Lois Lane. On his free time, he hangs out with colleagues and helps with the farm work for his mother. Developing relationships with the people of Metropolis, with his parents, and with the Justice League takes a lot of time and effort even for a hero like Superman.
When Batman found himself with Kryptonian powers, he essentially wiped out crime across the globe. He never stopped to eat, drink, talk, sleep, or anything else that human beings do. He had a complete disregard for government and Justice League authorities. Bruce eventually developed an extreme approach to countering crime and terrorism, and that led to him fighting old friends such as Nightwing and Wonder Woman. If you really want to know what it would be like to have a Superman who worked 24/7 without any breaks, then this is a really good preview. I believe the arc is Superman/Batman #53-56.
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