Employed persons do too. They just don't know it. Both halves come out of the employer's pocket and both halves are paid to obtain the employee's services. The only difference being two different descriptions on the paycheck.
I’ve always been for total disclosure on the pay stub.
When you ask most folks how much they make they’ll mention “take home”.
I think most folks would be surprised if the stub started out with “Net Worth to the Company this pay period” and then start through all the employer paid fees like Unemployment Insurance, etc, their half of SS and then running with what the people usually see.
Would open a few eyes.