Views differ. There are as many views on this topic as there are smart people. John von Neumann took the position that being in the world didn't necessarily mean being of the world:
"You don't have to be responsible for the world that you're in." -- Advice given by von Neumann to Richard Feynman as quoted in "Los Alamos from Below" in Surely You're Joking, Mr. Feynman! (1985)
I happen to agree with that sentiment.
Also, when smart people decide to engage with the world's problems, they often get it spectacularly wrong -- example Nobel Prizewinner Bill Shockley's brainless campaign to make people aware of the imagined inferiority of black people.
Albert Einstein famously turned down the presidency of Israel on the ground that he didn't feel that he had a head for the world's problems. In my book, that demonstrated his genius.
I think smart people don't necessarily know how to competently deal with everyday problems, and very high skill in one area doesn't necessarily translate to even average abilities in any other.