Why doesn't the employee have to pay the SUTA tax?

I think it is very simple. SUTA stands for State Unemployment Tax Authority. Why should an employee pay for the risk of being unemployed? Additionally, why should the lower income-earning entity (this being the employee, compared to the employer) pay for it?

The reason for SUTA (that being, unemployment) has not been caused directly by most employees anyway. Right there is a very good reason...