Sounds like maybe it would work for a while. A few problems/concerns pop right out at me.
1) If Joe has paid into SS for 40 quarters (10 years) and then opts out what happens if he becomes disabled in three years?
2) If Joe (currently age 40) now qualifies for SS (with a projected SS benefit of $2.5K/month at age 62) then he must consider that he will likely never accumulate private savings (in just 22 years) to beat that deal; yet Joe has absolutely no guarantee that SS will actually remain "as promised" when he retires in 22 years either.
3) My biggest concern is that as less and less voters remain in the "public option" form of SS then there is ever diminishing political pressure not to simply screw them over later.