Tbh, immigration isn't the worst "solution".

We do have an overpopulation problem. Well, an overconsumption times overpopulation problem, really.

We could fix that by either consuming less (which we apparently, as a species, really don't want) or by having fewer people (which we apparently really want).

So, in the end, reducing population isn't a real problem. Even if the population shrinks by 50% each generation (~25 years, for the sake of the argument), there will still be 250mio people left even after 5 generations. The trend should probably be reversed sometime then, but until then it's really not an issue on the species survival aspect and it would actually be really good for the planet and our long-term survival.

But until then we have mainly one problem: our economic system is based on infinite growth, which can't work. So again there are two main solutions: either we bring in people from other countries, who benefit from a higher standard of living here while supporting our economic system, or we get rid of the real parasites and freeloaders in our societies: the ultra rich. And again, for some reason we really don't want to get rid of the rich.