You can actually calculate how many years you would have to live to make up the difference.
If you would collect $20,000 at 62 and $30,000 at 70 (made up numbers), you would have lost out on $160,000 at age 70. It would take you sixteen years to make that up at $10,000 more dollars per year.
And that isn’t even counting the time value of money, AKA inflation.
And I figured like you did, that it would take years to recoup the foregone money I passed on at an earlier age and maybe impossible to ever catch up.
The government's run the numbers. They offer you a little more per month if you'll "wait", knowing all along that they will likely have to pay out less in total overall benefits since more people will die at an exponentially faster rate the older their age group gets. They don't have to pay anything if the recipient is dead.
I did all the calculations and rationale from every angle and they all pointed towards, take the money now, either before you can't because you die or you can't because the government has run out of money and/or has re-written the rules.
But take the money while you can and can spend it while you still can.