Imagine a factory that's dumping large amounts of arsenic into the public drinking water supply -- a factory that can't operate without doing so. Imagine also that studies show small amounts of arsenic are safe, but large amounts in drinking water can cause serious negative health effects. Seeing these studies, someone comes along and proposes a regulation that limits the amount of arsenic this factory is allowed to…
Poverty, poor education, etc are the underlying problem - the arsenic - and income inequality is one of the symptoms - like hair loss from chronic arsenic poisoning. Attacking income inequality directly would be like forcing haircuts on people to make wigs for people with arsenic poisoning. Not only does it not solve the problem - it helps a bit - but it actually harms innocent bystanders.
People like quick, simple solutions. It's a lot easier to raise taxes on billionaires than break the cycle of poverty or fix public schools.