Your repeating of another superficial, simple minded, and popular myth compel me to answer this one. Population stabilization (what you call stagnation) is irrelevant to GDP growth PER CAPITA (as opposed to aggregate growth). In fact, very low population growth countries that are shrinking like Finland, Taiwan, and Japan have been doing just fine or excelling on per capita basis, while most of the countries with very high population growth rates are impoverished dung holes.
More to the point, if quality of life is important, then you have to face the reality that the continued population growth of a country or of the planet means an accelerating need for more water from aquifers, rivers, and lakes. It means a greater and growing demand for energy, greater urban expansion, more density, more air pollution, traffic, and loss of land and open space. There are certain things there is only so much of (eg land) and unless you aspire to live in the density level of a crowded Japan or Hong Kong more immigration isn't a solution, its a problem.
The socalled "population problem" has zero to do with having more unskilled landscapers and dishwashers. It actually a temporary demographic concern of a bulge of aging non producers (eg baby boomers) and the declining numbers of young workers to fund them. And this problem is acute because at least some western countries created an entitlement Social Security system designed as an intergenerational Ponzi scheme. And like all such cons, it required a huge and growing base of workers to support many fewer retirees.
Moreover, what is often overlooked by non economists is that in addition to the retired old, there is the trend of extended childhoods, from the elimination of child labor generations ago to the increasingly longer period before grown children leave the home and become net contributors. And unlike the old and retired who do have savings and investments that provide the economy capital, "biff and buffy" only become tax net contributors after 25 (depending on their level of employment).
Now in the longer run baby boomers in the west will die off, and if support services are still shrinking then younger folk will have to get a job sooner. Frivolous, expensive, and unnecessary higher education will be less of a problem and society will benefit by no longer have less demand (and higher prices) on housing, water, energy etc resources .
