Investing Social Security in Stocks

Regarding proposals to "invest" social security contributions in stocks, either privately or in govt managed funds. Isn't it the case that those who have retired and don't work have always been supported by the current working generation. What's the difference between investing in a diversified mutual fund and living off the profits (and the discounted future profits) of current capital and labor, and having the government tax the inncome and profits of current capital and labor. Granted leaving investment decisions to the individual will result in higher transaction and administrative costs, and result in more risky outcomes for those who do not diversify, but wouldn't investment in a stock index fund be similar to the current system of taxing current income to support retirees?

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