Hell, that sounds WAY too much like work - and if I wanted to do anything resembling work, I wouldn’t be hanging around these boards all the time! 
There are a couple of reasons I don’t do what you suggest. First and foremost, working for SSA has given me some idea of how tremendously vast this program is. Tho I’m pretty much of an expert in my one area, there are aspects of SS that I know NOTHING about, even 20+ years in.
The other reason is that the information people most often want - inquiries concerning their personal accounts - is generally available to them other places. These days everyone gets their statements concerning recorded income and projected benefits. And if you have any specific questions, it is a relatively easy thing to call the toll-free number, or stop into your local district office. The Agency has allocated tons of resources over the past decade-plus to improve telephone service, and everything I have seen has shown that it has improved. And there is a TON of general, legal, and historical info readily available at ssa.gov.
I think the 2 points I mention here are relevant to what I believe is a lot of people’s distress concerning SS. They have difficulty reconciling their personal interest with the general goals of this program. You don’t need to go any further than the name - Social Security - to figure it is something other than simply an individual investment program. So it shouldn’t be surprising that you get should expect than maximum market “profit” from your “investment.”
IME a lot of people’s criticism of the existing system is based on their very narrow perception of their personal finances - which I believe may not be the best lens through which to judge a system intended to serve the entire population. Another point which you may consider as you wish - it seems as tho the folks who complain the loudest about what a bad deal SS is are those who are doing okay for themselves - with some personal savings and a decent middle-class or higher lifestyle. Whereas the folks who are the most dependant on SS are less vocal - and far less sophisticated in their ability to pursue other investment opportunities. Final statistic I’ll offer - 34% of all SS recipients 65 and older depend on SS as 90% or more of their income. Rather than worrying that some of those folks might be drawing more than they paid in, I prefer being glad that I will be able to avoid a similar fate.
Another factor of the size of the SS system is - like an aircraft carrier - you can’t spin it on a dime. IMO a program this large responds better to “tweaks” and gradual changes, than to radical overhauls. Take a look for a moment at the truly mind-boggling transition costs that would be involved in implementing the various privitization proposals, and consider whether that affects your opinion.
One final point I don’t quite understand about privatization - exactly how do you determine when you are going to withdraw your funds? If you are in your 30s you may not plan on retiring for another 35 years. But if you become disabled tomorrow, should your benefits be limited by how well you invested your contributions? Or if you die, should your survivors be similarly limited? And should the amount you and your survivors draw be determined by whether the market is up or down at the moment you die or become disabled?
My approach may be twisted. But I kinda figure that if I make enough money that I have to pay a ton into SS, if I am not poor enough to need to try for SSI, if I am healthy enough that I don’t need to draw disability, and if I live long enough to worry about whether I’m making back “market rates” on my SS contributions - well, I’d prefer to dwell on how damn lucky I am and how good my life is, instead of worrying whether someone else might have gotten “more than they deserved.” Just a mindfuck that works for me.
Now - I really should get something done…