Taken to its logical conclusion one could even argue that ending government backed retirement pensions entirely and letting people make their own decisions is the best idea.
Some people might plan to work until the day they drop, which is obviously a laudable goal. It's good to contribute to the economy.
Others may purchase an annuity for a target date years or decades in the future, which pay out in basically the same way as social security tends to.
Some (maybe most) would just save more for retirement, because they know if they don't no one will.
Realistically I suspect most people would hedge their bets dynamically go for a combination of these things. Which isn't all that different from the current system, where SS despite being over 20% of the federal budget is considered by most to be woefully inadequate even in the current day for a retirement plan.
If one accepts this hypothesis, then raising the retirement age is good for all previously-working people, as they now have less people to support and more workers providing that support...