It's rather obvious. There are even offices that collect the relevant statistical data.
> you can eliminate most physicists and mathematicians
No. Both disciplines are required by a lot of companies today. If you have a look at www.indeed.com there are currently 3.5k jobs for physicists. There are subjects where there might be a dozen jobs per year per thousand graduates. But engineers are missing everywhere.
That’s absolutely not their sole purpose.
And someone must take care of state bureaucracy anyway.
It is difficult to start a PhD worthy job in a new field at 66, as there's still a lot of domain specific learning (in the private sector), and most companies don't want to commit to making that investment in someone likely to voluntary retire, or quit due to health issues.
So, instead of working for 6 years, she got a very expensive degree that society is unlikely to benefit from, as there's often no way to apply these skills in the economy
Sure. But you complain that resources are wasted when retirees go to college and get their doctorates. I replied that resources are already being wasted on a large scale when there are academic studies that generate more economic costs than benefits. I have clarified my position in my further comments if you are interested.