First of all the System is NOT in Peril!
Sorry, you are explaining Averages, not for the individual Retiree. If a retiree is going to live to age 82 years, regardless of improved longevity, he'll collect less if you raise FRA.... You make the assumption that EVERY retiree gets to live 2 years longer when they raise the FRA! Do you understand that some retirees may not even live to Age 62?
Some retirees exercise, don't smoke and eat a balanced diet and will live longer regardless of the FRA .... People are not limited to collecting for 15 years! -- They collect until they die! --- If they start collecting later, then that is a DECREASED Benefit for them!
With logic like yours, ---- Do I have to explain it to you?