I think we should privatize Social Security but keep it under government oversight, investors and businessmen are obviously more responsible with money than the government, they would be inclined to make sound investments only, whereas if the government were left in charge of the Sahara there would be a shortage of sand.
The government is running out of money to put into social security and privatizing things like this will only make it better. It usually means lower taxes for the people and also gives people more choices. We put our own money into social security so it only makes sense that we get to decide what to do with that money.
Yes, privatization of social security will improve wealth, because it will give investors more say over where their money goes. Investments have a much higher return in private markets than they do in the social security system. Investing privately, people will have more money for retirement in the end when they reach retirement age.