And the other issue is that the productivity in care work is still rather low. So we have to put quite large part of work force to something that is for general economy unproductive.

Let's name the elephant in the room: No government is going to make a significant part of the workforce work in (unproductive) elderly care. Societies will eventually start to just get rid of their old, first encouraging life-ending treatment, and eventually enforcing it if there are not enough takers.

The counter to this argument is that time begets wealth - thus the oldest folks are the most likely to have capital. Those with capital impact economic decision making: thus the real trap is that we will all eventually spend all of our time taking care of the elderly - it will be the last job in town - as the elderly will have the last wealth at the last moment. Government policy of today certainly favors the old and wealthy - why should that not continue?

Depends on capital they hold. Capital only has value because there is either demand or it produces something. If everyone in town is working to take care elderly, the capital in factories is worth nothing as there is no labour to produce things. Or the houses are worthless as there is no demand for them. Later can already be seen in certain locations. So they are out of luck unless they own the nursing home or production for necessary goods in taking care of them.

It will not continue because it is ultimately unworkable. We are seeing that already today, with increasingly larger parts of the population becoming aware of the "boomer problem". Eventually this will become evident enough so that governments can no longer ignore it.

That being said: Capital of a few old people becomes pretty meaningless when your economy is collapsing. See any country that went through capital collapse in the last 100 years or so.