You're advocating for higher income tax. I'm shocked.
Structure it like the lottery where you can take a one lump payout at a reduced rate, or take annualized payments. Make SS an actual investment program. Think of ways to grow the pie that don't involve taking more money out of the pockets of Americans.
It's not gambling or an investment program. It's more akin to insurance.
I do like your idea of doing things with the age of claiming benefits. For example, I'm not taking Social Security before I reach age 70 because payments increase 8% for every year I don't. At age 70, I have no incentive not to take my benefits, even though I won't need them in order to live comfortably. If I had the option of deferring benefits beyond age 70, with benefits still increasing by some percentage, I might choose to bet on my own longevity by waiting. If the fear of most retirees is outliving their money, it seems like an idea worth considering.