In my observation, there are a lot of unaccounted for and unintended issues that can arise from this.

Where I live, we are going through a lot of this right now (98+% of population growth is from immigration).

Immigrants have more kids than the non-immigrant population, but they do not actually have above replacement rate amounts of kids, so they are going to require more immigrants to take care of them later on. Also, the children of immigrants have non-immigrant level fertility rates. So, it's not a long term, sustainable way to "replace the aging population."

On top of this, immigrants often want to bring their elderly relatives with them when they are possible. I know there are some ways to try to mitigate this (e.g., immigration limits, charging them extra fees on immigration), but at some point there becomes a large enough immigrant voting bloc that this changes. Now you have extra, unaccounted for elderly people that are required to be looked after.

I have no idea what the solutions are, but if we are trying to plug the gap through immigration, it'll require perpetual immigration. Most countries globally are now at below replacement fertility rates, so this opens up a huge can of worms. I'm sure I'm missing something obvious, but it doesn't seem like anything other than a quick band-aid or a solution that's doing anything other than adding "debt" to the issue.

Where do you propose regularly finding hundreds of millions of skilled English speakers of similar values who are interested in permanently migrating to what will be countries clearly in decline?

India, that's where everyone else gets them. People are just economic units

Even India's fertility rate is now below replacement, and they're increasingly actively working to turn the tide on their brain drain. And India's economy is both already massive and growing quite rapidly. At current trends they'll pass the US within a decade or two. They certainly aren't just this long term sustainable pool of people to draw from.