So, here's what is totally wrong with your simplistic analysis.
1. Your analysis assumes that the bulk of the money is in stocks for a 40 yr period. 1. Stocks don't EVER grow in a straight line. Stocks have have been know to not do shit for 16 years then surge. Returns have been incredible boosted by a highly stimulative fiscal and meenetarypolicy that makes returns look attractive. Are you that certain that stocks will grow 8% over the next 40 years???? Wow, Ive got 35 years working experience running major institutional portfolios. That is fantasy.
2. in retirement you have withdrawals that are infrequent, small & large, very spotty and hard to predict. I dealt with those as an institutional portfolio manager. I gotta tell ya, this can help, or they can kill ya. This is an asset liability management and cashflow needs problem; my specialty. That for one, makes your return expectations highly inflated. And this risk is huge. You gotta beat me on returns! Im a professional manager with 35 yrs experience. Remember Clint Eastwood? In speeches I used to quote him. Remember what he said? A man had to know his limitations!!! I know what you're thinking' was that 5 bullets or 6. To tell ya the truth, I lost track myself. So the watch word is modesty regarding your abilities to truly generate a n 8% rate of return, despite the bullshit ya hear and read on the internet. You only hear about the winners. That is called "dropout risk".
3. Social Security takes out inflation risk and mortality risk. Mortality risk, I'm sure you know, is the risk that you outlive your assets. Mortality risk is HUGE. You are totally naive if you minimize this. And we will have Biden and the Congress for a long time, and we are gradually pulling away from cheap chinese crap. So, the risk of inflation continuing is a given.
4. As I said, Social security is a huge handout, including Medicare to the middle class. You get out 2-3 times what you, your employer, and risk-free interest would have accumulated over a 40-year period would have put in. There are various studies by actuaries on social security and its value. I used to have friends that were pension actuaries, and I'm a retired CFA from a major institutional investment advisory.
5. The public has numerous misconceptions, like somehow the rich ar getting something more from social security that they didn't earn and their ss taxes are capped. Their benefits are capped and drastically cut back.
I could probably write 20 pages on this problem of asset/liabilitymanagement and pension management.