Earlier quoted context omitted.
If you permanently reduce immigration, including deporting unauthorised migrants, you can achieve both of those things. Given the cost of land and building, we should consider Western nations 'full' and only allow immigration 'swaps' from other highly developed countries.
The issue with this though is two fold: 1.) You cannot have a nation of college degree high skilled workers. At least until robots and AI are widespread. Being rich is a lot less fun when you cannot spend it anywhere, because none of those places have a staff. 2.) Since people aren't having kids, and we love to saddle the future with liabilities, someone has to fill that void. All the hot shot AI inventory management…
https://www.cedefop.europa.eu/files/images/graph_month-stat_...
2) Fertility is heavily influenced by the availability of housing. Without immigration, house prices will fall and wages will rise, providing a boost to fertility until the population equalises.
https://www.nber.org/digest/feb12/impact-real-estate-market-...
With mass immigration you shortcut that, and simply end up replacing the original population, probably with negative overall effects if the incoming population is not genetically (average IQ, predisposition to violence) or culturally (respect for women etc.) aligned.