Yes, the US does have an employer withholding system but there are so many more layers of taxes and complexity because the taxation system is less federalised.

In Australia there is a single federal employment tax, and a single federal sales tax. States and counties typically collect property tax and fees from services.

In the US both the federal and state governments collect income tax. The tax rates and deduction complexity varies widely between the 52 states. Then the states AND counties (districts) have different sales tax rates. California alone has over 1790 districts each with sales taxes set at a local level.

Not to mention capital gains, Medicare tax etc...

Then the comparatively high lobbying, wealth inequality and inefficiencies in the US political systems makes tax change very slow or regressive.

*I'm an Australian living in the US