Inequality is something I see as necessary for two reasons, but something which should only be allowed to a given extent.
First, inequality is needed so that there is a reward for working harder, doing more. The one who coasts through their education doing only the minimal needed before getting a job doing the same should be rewarded less than the one who gives it their best. BUT, inequality should never be so great that the kid who coasts can come from such a privileged position that they are forever in a better position than someone who works hard. For a lot of American's, working hard doesn't really get rewards, so you could say we have exceeded the optimal amount of inequality and thus need more equality. But if we envision a fully equal system where everyone is equally rewarded, there is far less incentive to do more than the bare minimum. Even supporters of basic income think that those who go above and beyond should be rewarded with extra income above the level of basic income. I've never heard of anyone supporting a basic income plan where all income beyond the basic income level is taxed at a 100% rate. Even a 50% or 75% tax rate indicates those who do more should have more, with the difference being how much more.
For this, we need to make sure the inequality is high enough that effort is rewarded, but keep it low enough that birth does not convey special privileges.
Second, equality will never exist in all areas of life. Even if we had total financial equality, some people are more sociable, better looking, etc. As such, what people have access to in our society is still unequal. In a financially equal society, the one with vastly superior social skills, or who is attractive (look up the Halo Effect), has access to more resources and thus inequality still exists. Allowing some level of financial inequality allows people a way to do better when they lack the above skills.
Consider some modern day developer who is slightly autistic but highly functioning enough to hold a good job. Their ability to earn more can, to some extent, help offset the lowered levels of social skills in the extent it allows them to achieve their life goals.
The only way to have full equality beyond just financial equality would be to implement a tax on anything that can be considered a good or service in the most abstract of methods, and I think we would find that even the most ardent communist are all out libertarians in regards to these social goods and services.