Not if the payroll deduction went into the 401k, instead of going into the government maw.
Yes, but one would then have a political problem with restricting them from taking money out of their 401Ks—yes, I know, we could do that and are doing it with Social Security as currently constituted.
What I would fear is that the politicians would buckle and we could end up with a worse system, i.e., political pressure brought to bear to allow people to foolishly drawing out their retirement savings long before retiring. Then what? Let them starve or institute yet another huge government program?
Yours is a sensible idea. But there could be major problems if the courts rule that it is their money in the 401K accounts.