The US tax system is composed of so many different taxes: FICA, Income Tax, Medicare, cigarette, gasoline, unemployment, AMT, etc. I'm sure that just scratches the surface.
The reason why we have so many taxes is that everytime Congress creates a new program, they have to create a tax to pay for it.
Simplify! Develop a small number of taxes. Income, Sales, VAT, whatever. Then adjust the rates on those taxes to pay for the programs.
The current litany of taxes on payroll are a huge problem. An employer is faced with so many reporting and withholding requirements that they are reticent to hire employees. They also end up being regressive instead of progressive.
The combination of a tax on consumption (preferably on both goods and services) plus a much simplified income tax should be designed to generate the needed income.
The only payroll tax, other than income, should be an employer paid tax that is based on what benefits the employer provides. The theory being, if the employer does not provide the benefit, then the government will have to. The employer could pay a tax that ranges, say from 0-10%. Offer health insurance, pay less tax. Pay a living wage, pay a lower payroll tax. Employ people only part time with no benefits, pay more tax.