Imagine another country which has government-funded secondary education and pensions that cover the bulk of retirement expenses. Wouldn't the "necessary" inequality be noticeably lower in that case?
In fact, in the real world government pensions tend to increase apparent wealth inequality, since they are usually capped (e.g., in Canada the CPP pays out a proportion of your first ~$40k/year of pre-retirement income, but ignores any income beyond that point) -- in order to maintain the same standard of living post-retirement, the wealthy need to save a greater proportion of their income.