I would cross income inequality itself off the list of priorities. Far greater concerns include: absolute suffering among those with low incomes; a socioeconomic structure that seems to be ossifying into a hierarchy of professional classes; and a decline in income mobility, which is to say, in equality of opportunity. It doesn’t really matter whether Bill Gates has some incomprehensible sum of money at his disposal. It does matter a great deal whether there are Americans in desperate want. And of course, it matters whether anyone with the aptitude and motivation can become the next Bill Gates, or only a handful of privileged people who are already well off.
I also submit that the importance of the issue is inversely proportionate to the ease of solution. The government is very good at taxing income of some Americans and writing checks to others. (Whether you think it should do this is, of course, a different question.)[JC: Actually, I'm not so sure the government is very good at this. Our tax code is a mess. Our income transfers largely go to middle class and well connected businesses. Our system of writing checks includes numerous 100% + marginal tax rates and other disincentives. Despite the one of the most progressive tax systems on the planet, there are still schizophrenics on the streets.]
It is very bad at preparing someone to live a solid and fulfilling life of work and community, which is one reason we mostly leave that job to parents.
Government is also not well suited to creating a lot of satisfying and remunerative jobs. It can contribute to productivity and help companies to flourish, for example through basic research and by maintaining a competent legal and regulatory system. And it can directly create a few jobs providing government services; these have been, for many communities at many times, a stepping stone to the middle class.
... For the most part, the best the government can do is to avoid stepping on the creation of satisfying and remunerative jobs; no nation on earth seems to have figured out how to generate “good jobs” for everyone.[JC: I think she means no government on earth.. "nations" have figured it out!]