#1, by collecting SS at 62, you can keep more of your investments intact, earning more money. The cost of deferring and getting the larger monthly payment at 70 is that you get $0 between 62 and 70. Your "analysis" totally misses this.
#2 Some people think that the benefits will change and nobody gets grandfathered in, such that you are better off getting the full benefit while it's still being given out. If you can get benefits at the current rate at age 62, but at age 69 they cut everything by 30% across the board, your breakeven point has been pushed quite a ways out.
There are a lot of other moving parts:
- Being able to convert 401K to Roth at a lower tax rate
- The tax impact if you can't convert it all before 70 and have to take MRDs,
- How much of your SS gets taxed in various situations
- Whether you are trying to limit income to get an ACA subsidy
- Your likelihood of living past the crossover point based on your health and your family history
- Special spousal situations
- The state of the stock market: If we're at a high, I'd rather be selling off a little more of my investments for living expenses and deferring SS. If the market drops, I'd rather limit my selling, and would likely take SS to cover more of my living expenses. Don't forget, you can make that decision at any point between 62 and 70, so if you are 62 now and think the market it high, you can hold off, and then if it crashes in 2 years you can start collecting then. There's no formula for that, just like there isn't one for #2 above, you go with your gut feeling of what's best for you
- others?
The good news is, most of these probably don't matter too much in the big picture. I think because it is an active decision you have to make, people (myself included) overthink this too much. I have a hunch that if the govt just automatically started giving you your SS benefits at 67 unless you explicitly told them otherwise, a lot of people would just passively accept it because then they wouldn't have to make a decision.