Actually, no. If the government of Equalland were to pay a $50k/year to each retired couple, they would need to save less and the entire graph would shrink vertically -- but the ratios would stay the same.
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.
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.