The Chilean retirement system was created on the advice of the late great Milton Friedman.
After the socialists were deposed by Gen. Pinochet - Pinochet set out to create economic reforms that would result in a more stable country. He was fairly successful. Later, after Pinochet stepped down, the voters tended to lean towards socialists - but the socialists have to be careful not to destroy the retirement nest eggs of millions of voters.
This is a big reason Democrats don’t want any privatized social security system, because any economic down-turn that hurt the market would hurt retirement accounts, which would result in voters taking the retribution on politicians who had steered a course away from forces that keep the markets healthy!
The Chilean social security idea is a great idea ....but credit belongs to the American - Milton Friedman.
There's another big reason: both Democrats and Republicans have been borrowing Social Security funds and using them for other purposes for years, in order to buy votes for themselves.