I'm not saying that immigration is bad.
However, having a country advocate zero childbirths - and trying to keep population up entirely foreign migration is a recipe for disaster.
Presently a relatively small fraction of western populaces can afford children without assistance. Trying to artificially prop up birthrates is putting a bandaid on a gushing wound of wealth inequality. If productive gains weren't being realized by capital to such an absurd degree more people would be able to afford doing zero-revenue labor like raising children for longer periods of time.
In Australia, we call it the population (or migration) Ponzi.
Another way to look at it is - you're essentially borrowing from your future generations, in order to fund your current lifestyle.
Those future generations are going to be the ones looking after you in your old age (through being taxpayers to provide services - or in some cultures maybe even literally being the ones to house/care for your), and also because that's how your culture/society continues. Society/culture is more than just a input/output machine that eats, s*hits and sleeps.
I don't particularly like the arts, but I understand that as a whole, our government funds things like that for the betterment of society.
I am fortunate I don't have any major disabilities - but if I did, I know my society looks after those less fortunate (or I hope they do).