Yes, this is a fundamental misunderstanding of social security. Social security isn't insurance or an investment, it's a tax that's presented as an insurance or investment in order to make it more palatable. The social security tax rates were set with the demographics and life expectancies in mind decades ago. And now that these demographics and life expectancies have changed we'll either have to drastically increase the tax workers are paying, or drastically cut the amount that people withdraw.
I prefer what we have here in Australia where you are required to pay money into an account that is actually yours, with a balance that you can watch grow, and that you can withdraw as you need when you retire.
The Age Pension is designed to support the basic living standards of older Australians. It is paid to people who meet age and residency requirements. It is targeted through the means test to those who need it most. Pension rates are indexed to ensure they keep pace with Australian price and wage increases.
If you only have the house you live in (that's more or less median) and no income (from additional rental properties | other investments) then you might qualify for a pension.
Typically people might draw on their superannuation fund to provide a weekly income for themselves although they are free to use it for their retirement plans as they see fit.
I don't know if I agree with your example figures. SS was meant to be self-funding, and lately it hasn't been. This is partially because people are living longer.
Furthermore, the decline of pensions and rise of the 401(k) has enabled Americans to blow their opportunity to save for retirement, often on things like housing and college tuition (but that's another topic).
I think that either SS needs to be THE retirement plan, or it's the 401(k). As someone who maxes out their 401(k) each year, I do not want to participate into SS. I don't want it taken out of my paycheck, because that money would otherwise go into my 401(k) (technically), which I have more control over (where it's invested), which I can draw from in case of hardship, and which I can access at 55 1/2 instead of 65.
I do think SS is a good safety net to have, and I don't necessarily want to be disqualified from it because I "opted" for a 401(k), but realistically SS payments are so low relative to the cost of living that if I found myself living on it exclusively, I'd probably be only slightly more-comfortable than if I didn't have it. It's a shitty retirement either way. You're definitely not traveling or eating out or anything like that.
Is that a fundamental misunderstanding about what the purpose of SS is?
And not sure if you know, but the dollar figures are more like you could at most have paid about $300k into the program over your 40 year working life (if you maxed out the contribution cap, 6% tax on $167k currently), not $1m by a long shot.