This article provides some valuable insights into how OECD countries use tax and spending policies to reduce the effects of wage inequality. The US has the one of the more progressive income tax policies, but it is near the bottom in the use of transfer payments to reduce inequality. Transfer payments in the US are 9% of income compared to the OECD average of 22%
While the US income tax is relatively progressive, it would be less progressive if the payroll tax tax were included as a tax on income. The payroll tax only applies to the first $108,000 of wage income, therefore it is a regressive tax. The US collects almost as much income from the payroll tax as it does from the income tax. The government does segregate payroll taxes from income taxes when it spends money, or when it calculates its budget deficits. The Treasury simply puts an IOU in the Social Security trust fund when the government spends the surplus dollars that were not used to provide benefits to SS recipients.
Many OECD countries use a value added tax for much of their tax revenue. When combined with the income tax, they collect more tax revenue than the US, but they spend more of the tax revenue on things like education and healthcare than the US. Their more extensive use of transfer payments has a bigger effect on reducing inequality than does the more progressive US income tax.