Your description of SS is about accurate. Rising life expectancy and population have flipped the program upside down and it just doesnt adequately pay for itself anymore. The problem to adjust it now comes primarily with the fact that our generational populations have these massive booms as opposed to growing at a steady rate. Our government is only beginning to come out of a period largely dominated by people of the post world war II baby boom.

3 of our last 4 presidents (spanning almost 2/3 of my 31 years on this planet) were born within 6 weeks of each other in the summer of 1946. Government has been slowly getting a bit younger, and the generation apathy of Gen X seems to have less of a voice than the millenial boom, but largely WWII baby boomers seem pretty unwilling to modify the program currently, as it stands to remain solvent to the end of their lifetimes. And they still largely control government, as post positions have age restrictions.

What you have as a social program sounds similar to an IRA or a Roth IRA in the US, which are optional retirement investments rather than required social security, but they work similarly to what you're saying.