should simply have more children
Dissolve free trade agreements, restrict immigration, penalize offshoring of jobs, shorten average education length and greatly cut down the number of students of non-value added (read: useless or not in demand) majors and finally kill off the for-profit housing real estate sector (a private person renting one spare apartment is ok, a for profit corporation owning whole buildings is an abomination, especially if it is foreign-owned).
This should take care of high housing costs, low wages and settling down being delayed too much due to them or education. Not everyone will be convinced even if the economical circumstances for starting a family are ideal. Those however that do want to have one should have the conditions to have as many kids as possible. It would anyway be easier to help them than say convince a generation of women raised on shity anti-family entertainment that partying until your 30s (or 40s) is a bad life choice.
will ever allow their country to to turn: first, into a huge nursing home and second,..
I'm inclined to believe that it's a false narrative.
It's upheld by the axiom of population "stagnation" or slight decline, being bad because of various reasons. The reasons don't matter so much, you can list them if you like, but the bottom line being that this is a "crisis".
Therefore, to solve this "crisis" we have to import people into these societies, lest "bad things" happen. See, the various reasons for why this is a "crisis".
In reality, the natural population of any species must reach an equilibrium. This is imperative and unavoidable.
So why is reality being dismissed in favor of a crisis narrative, that's the real question.