There are a number of problems with what you propose.
First, unlike an HSA and an IRA, Social Security is not a pool of money that individuals have access to. The money is managed by the government. Therefore they have strict legal requirements on what actions they can take.
Second, derivative markers are much more risky than the current fiscal profile of the Social Security fund. Yes that means Social Security can have huge gains, but that also means Social Security can have huge losses. Social Security is supposed to last over your entire life. How would you feel if after 50 years of contributions the Social Security fund lost half its value because of a bad trade?
In general Social Security knows all the numbers it needs to survive: how many people are contributing, what the total contributions are, how many people are going to retire and when, how many people are retired, etc. Its a lot of big and complicated numbers, but you can put it all together to get a reasonably accurate estimate of the required growth rate to sustain Social Security. Why risk more than you have to?
Another less obvious problem is liquidity. Even though social security has been cut a lot, its still HUGE. Its going to be hard to put all that money into a type of financial security just because there may not be that many people selling. And if the Social Security fund decides its a good time to sell its derivatives it may have trouble to sell them all for the opposite reason - there just may not be enough people buying (this is what lead to the Lehman collapse in 2008). You could offset this by working in many different types of derivatives, but now your operational expenses balloon as well as your risk metrics.
So short story, Social Security going into the derivatives market would be theoretically possible, but realistically impossible.