Income/Wealth Inequality; Why does it matter? I have attempted to answer this question on my own through reading books, blog, and other economic pieces of literature but they all fail to articulate why wealth or income disparities matter. Now obviously leveraging slave labor or paying someone literal pennies is an issue. But why does the disparity of wealth between say the middle class and the top 1% matter?

From what I have studied it seems cultivating a competitive market (fair prices for goods and housing), managing inflation, and ensuring a strong currency is really what is necessary. Given these things everyone would be able to buy and sell goods or services and still be able to squirrel some money away for retirement. What am I missing?
There could be some complicated models where high inequality could have effect on efficiency - the research is inconclusive (or to be more precise almost non existent) on the matter.

However, in Public Economics, depending on the selected welfare function (ralwsian, utilitarian, charitable conservative/libertarian etc.), inequality matters for optimal taxation. For example, even in competitive market without any imperfections someone’s marginal product of work and hence wage might be close to zero or not enough to afford food. From pure efficiency perspective that would be optimal, but under Ralwsian/utilitarian or also some other welfare function there should be some transfers to said person.

This being said economics does not provide any answers into which welfare function is the right one for that you need to study philosophy. Inequality as far as currently understood is a matter of taste.