The issue with trying to do that is inflation. If you were building a system from the ground up, you might be able to architect something a little more private (similar to a 401k model), however, the system was designed with the inflationary model in mind, thus the reason it was designed to allow for the current labor force to pay for the current retirees.
Unless someone is really savvy with investing and can target the right investments that will give them a return that exceeds the current rate of inflation, they'll end up being behind the curve come retirement time...because if you just took that money and put it in a basic savings account, the interest you earn wouldn't offset the inflationary devaluation of the money you have in there.
While this is in no way an endorsement of our current SS model (I personally don't like it)...just simply saying that trying to convert at this point in the game could have some disastrous effects.
To put it in a little perspective...
If you took $500 today and put it in a basic savings account, in 40 years from now, you'll be sitting on ~$1,100 dollars based on current interest rates.
If the next 40 years are anything like the last 40 years in terms of inflation rates, that $1,100 in 2055 will give you $248.86 in equivalent 2015 buying power. (IE: you just lost half your buying power)
In order to ensure that your money would hold it's value on par with inflation, you'd need to have your money in investments that would consistently give you 4%+ return rates.