While what you say might sound like a good idea, there are deeper underlying issues. First government employees cannot actually contribute to their retirement, hence the term UNFUNDED ENTITLEMENT, because government does not generate income, only expenses that must be paid by the working private sector and businesses.
Second, government employees get more than one UNFUNDED ENTITLEMENT. Not only do they get their government retirement check they also get social security. Many government retirees also get second and sometimes third retirement check; called double and triple dippers.
Third, government payroll deductions (starting in 1983) for social security are spent then the private sector is taxed again to pay the entitlement.