Not to serve the purpose of social security, which is to serve as a minimal fallback defined benefit pension to to mitigate the effects of old-age poverty in the event that personal retirement savings fail due to investment risk (either by failure of personal investment, failure of private pensions, etc.)
It would be a nice public subsidy to the financial services industry, which is why that industry and their political proxies keep recommending this, but it wouldn't actually serve the purpose social security is designed to serve.
> It would be quite a bit less draconian than the government simply confiscating the money.
Not really; either way the government is seizing the money and directing its use.
There would obviously have to be a transitionary period where the government makes up the shortfall, in order to honor the commitments made to retirees. It would be painful, but only a small addition to the 87 Trillion in current liabilities of the U.S. government.
http://online.wsj.com/news/articles/SB1000142412788732335320...
Thus if you replace these systems with mandatory investments, you are reducing their available cash.
Everyone who gets a paycheck pays their 6% in social security, regardless of income level.
Social security tax is 12.4% on the first $113,700 of wages or self-employment income, and 0% on income from all other sources and wages and self-employment income past the first $113,700, so, no, you don't pay "6% in social security, regardless of income level".
(Note that on wages, but not self-employment income for obvious reasons, half of the 12.4% is paid as 'employer share', so that the employee never sees it, so it might appear, if you look only at wage withholding, that the rate is 6% -- or rather, 6.2% -- but that's not accurate.)
Oh, the irony.
You could have enforced diversification (certain percentages allowed for high vs. low risk), and accreditation boards to vet and approve mutual and index funds.
Also, the investment would have a very stimulative effect on the economy, and you could probably also set it up in such a way that it works on autopilot (like a 401(k)) for those that can't be bothered..
It would be quite a bit less draconian than the government simply confiscating the money. In the private sector, the current setup would rightly be called a ponzi scheme.