If you begin taking SS at 62, isn't your total SS eqivalent cash flow at 90 the sum of your annual SS payment (determined when you started at 62 plus COLA's) plus the investment income from prudently investing all those dollars received since you started collecting at 62? That is, to keep the comparison apples to apples, you have to assume that SS income collected from 62 onward is retained and invested and available when you are 90.
I prefer to keep my pension/SS separate from my investments for analysis purposes. Anyway, I think that the increased cash flow will be investment dollars I don't have to touch. But that is not the way I think about it.
For one thing, in my case, I will have a 10 year pension. So if I retire at 60, the pension will allow me to defer my SS to 66 or 70. All the scenarios I have modeled show a better residual, at age 90 (my planning limit) with deferring SS while keeping all other factors the same within each scenario.