Existing citizens are working less (and paying less taxes), and thus having less babies. And that long term trajectory doesn't sit well with the welfare states of the world that are getting deeper and deeper into debt.
Simply put, they desperately need more tax payers coming into the system to not only replace the ones dying off, but to breed new ones. Thus opening up the borders.
Remember, the welfare state is one giant Ponzi scam, that requires ever more scam suckers coming in. When that stops, the whole thing collapses.
https://insight.kellogg.northwestern.edu/article/economic-impact-of-immigration-in-the-us
The magnitude of the results was striking: if a county that experienced no immigration during this period had instead experienced median levels of immigration, residents today would have a 20 percent higher per capita income.