1) We don't care about wealth distribution per se. What we actually care about is utility maximisation (in other words, maximising the sum of 'human happiness').

2) Once we get pass some basic wealth level, to meet some set of basic needs like food and shelter, a person's utility is a function of relative wealth rather than an increasing function of absolute wealth.

3) If you accept points 1 and 2, we therefore should care about wealth inequality in and of itself.

There's also probably another argument to be made along the lines of 'decreasing marginal utility with respect to wealth'. Which is a fancy way of saying: a poor person derives greater utility from an additional $1 in wealth than a rich person does. This would mean that the sum of human utility is increased by taking $1 from the richest person and giving it to the poorest person.