The Larry White Privatization Plan

I would enthusiastically endorse the Larry White plan if it was possible for the state to credibly commit to refusing benefits to people who fail to invest.
Here's Larry's idea:

Here's how it works: we give Ms. Smith, a worker, the right to opt out of paying $100 in social security payroll taxes provided she also opts out of (say) $103 in future Social Security benefits. She can now save her $100 privately. She will consider herself better off opting out if she thinks she can earn a return of better than $103 for each $100 saved. Voila, who could object?

Maybe we can throw in a little benign paternalism, and have the payroll taxes automatically roll into some kind of investment account by default.
Anyway, nice idea.