Some of those points are very valid, but I just don't think economists believe there is any relationship between older people retiring and younger people participating in the labor force. If there is a correlation, and it might be easy to put the numbers into a statistical processing software package to show a correlation, there is no evidence of causation.

What would be the implication if you were right about how causation worked? The prime working age participation rate is increasing, in part, because more people are retiring or staying in school. This is creating a situation in which employers are posting more jobs because there is a certain amount of work that "needs to get done". What would that tell us about the health of the economy? Well, at worst, it sounds pretty neutral. At best, it sounds like a positive note. People that actually want to find jobs are having an easier time of it. People that don't want jobs are enjoying their golden years or staying in school. I am not sure how this is bad for the economy.

I think it is a mistake to look only at prime age labor participation and ignore total participation rate. To put it in extreme. When you have a million old people not working and ony two young people who are both working than you have a 100% prime age labor participation rate but still have a problem.

One issue you run into here is that there are far more prime working age people than there are retirement age people. Moreover, there is a reason we care more about the statistics for prime working age people. Old and young people tend to drop out of the labor force for reasons that have nothing to do with the health of the economy. Mainly, they retire or go to school. The prime working age participation rate gives you way more information about the business cycle. If we are trying to figure out to what degree the economy is in expansion or contraction, narrowing the demographics like this controls for an important confounding variable.

The fact is that prime age labor participation has declined since the financial crisis and unemployment went up since the financial crisis. I don't think this is a coincidence.

I know you are aware of this from the context of the rest of your post. I just want to reiterate that for months, arguably a couple of years, it has been the opposite. Unemployment has been trending down and prime working age participation has been steady or increasing.