Re: delaying SS and thinking of it an an annuity.
That's a very restricted annuity. You don't have any freedom to choose the monthly amount (and hence the initial deposit). You have exactly one specific monthly amount, which is determined by the SSA and you cannot pick a different amount.
And the entire deal can be changed at the stroke of a pen, by Congress changing the law.
With a normal annuity you can pick whatever benefit you want.
The company cannot change the deal unilaterally -- although they can go bankrupt and leave you with nothing.
There's an upper limit to what you can buy, but not a lower limit.
To my mind, taking SS at 62 is the lowest risk (bird in the hand). By delaying after that, each month you are paying SS the amount you would have received and using it to buy a small annuity. You can do that until age 70, so there is plenty of flexibility.
As far as saving portfolio withdrawals, they will be lower early if you take SS at 62, but higher than they could have been when you reach 70. If you take SS at 70, portfolio withdrawals will be higher early but lower after 70. There is an implied return rate that makes the two choices equal for an average life expectancy (or your own custom scenario), and for SS it is usually a pretty substantial return. It can be higher than many here seem to assume for market returns, but lower than others assume, and is probably higher than any of us should be assuming for bond returns. If you think market returns will be low, take SS late. If your market assumptions are higher, take SS early. Either choice can result in higher spending throughout retirement (62 and beyond) depending on the assumptions you are making.