No, payroll code must track fed, state, and local tax rules in order to calculate employees' paychecks and payroll taxes due.
Also, instruction for payroll deductions are pretty simple[1]. Usually everything you need is on one page. Plus a very short list of exemptions (401(k), HSA, FSA, cafeteria). Nowhere near 11,000 pages of tax code.
"Payroll deductions are pretty simple" is not as true when you require nationwide support. The Yonkers residency tax, the Indiana counties payroll tax, etc. are not as simple as getting the employees' states and running calcs. Add in non-tax deductions (401(k), wage garnishments, worker's comp) and you've now found yourself in an interesting world.