That would only move the problem of “there are too many houses” to cities or suburbs, not solve it.
Also, I don’t think empty houses are the main problem. An older population costs more and pays less taxes.
So, if one keeps current infrastructure spending, budget deficits will increase, and government debt will go up.
And if the population shrinks, government debt per capita will go up even more.
If their population really halves, I think many countries will have to make hard choices as to which villages or even cities, and roads leading into them, to abandon.
I can’t find it now, but I remember some people arguing Japan should do that with Fukushima after the tsunami.