There are two possible goals with SS: 1) buy the optimal amount of longevity insurance for a given input, or 2) optimize your total amount of SS benefits. Both are valid goals, but let's assume you want to prioritize the former.
The clearest way to think about this is to imagine a pair of 62-year-old twins, both of who are entitled to $3,000 per month at age 70, which, coincidentally, is also their living expenses.
Twin A defers SS to age 70, when he will get $3,000 monthly benefits. He must thus cover 8 years of living expenses to get to age 70, costing $288,000 in real terms ($36,000 x 8). After he pays that liability, he's home free.
Twin B also has $3,000 per month living expenses, but decides to take $1,705 in SS at age 62. Thus, he has a $1,295 per month of shortfall until he dies. To cover this with a joint-survivorship inflation-adjusted fixed annuity costs approximately $438,000.
The difference between the two is $150,000. That's not chopped liver.
I'd even go so far as to recommend that if twin A runs out of money a year or two before 70, he should max out his credit cards to make it there.
Best,
Bill