It’s a payroll tax holiday, not an income tax holiday. It’s intended to benefit the employer (who pays a matching tax for every dollar paid by the employer) as much as the employer. It’s the FICA/Medicare taxes they’re suspending, not the Federal income tax.
Ok, I’ll take your word for it but withholding actually is a payroll tax. It’s one of 4.
From Bankrate.com
“There are four basic types of payroll taxes: federal income, Social Security, Medicare, and federal unemployment. ... The employee pays a 6.2 percent tax for Social Security expenses and 1.45 percent for Medicare. The employer must match the deduction and send the total amount to the IRS.”