A lot of elderly Japanese already keep working well into old age. Some do it for health reasons (physical and mental), financial reasons, or out of something like civic pride/need to contribute to society. The problem is the sector of jobs that elderly people can't do.

It's just biology. People in their 70s and older are very likely to have physical and/or cognitive issues that substantially reduce their potential productivity. This is one of many reasons we should prioritize preventing and repairing the effects of aging, but until that happens it's going to be a problem.

It's just fear mongering, maybe they are like 10% less productive every decade-group after 60 on average, but it's hard to tell considering people leave the work force at 65. I'd wager that they are more productive on average than 20-30 year olds unless they have dementia.

Having an older population is only a problem if want unskilled labor to remain cheap relative to it's social value. The whole world has seen from America that relying on an immigrant underclass creates too many negative externalities for the price saved, I doubt Japan will copy this plan, they will just bite the bullet, pay more, and then act surprised when NEETs decide to work.

I don't see many of my 40-ish age who live healthy enough by exercising, going to work by bike or walking instead of car, so they can still be active, let alone productive when they enter retirement age.

I'm not sure I follow your comment. It's possible that AI will change the idea of who can be productive, just as the internet has changed the idea of who can be productive (people with limited mobility, for example).

Oh the productivity fallacy. AI making your job easier and saving you an hour a day doesn't mean that you'll spend this hour to do sport or even be able to use that hour as you please. We have cars (after trains, bicycles and horses) to get faster from A to B but at the same time the commute to work has grown. Many machines have been invented over the last millennia, yet we use this gain in productivity not to have more leisure time but to enforce consumerism onto the workers.