The problem is that (the current form of) immigration doesn't solve that issue. I'm not intimately familiar with other countries, but Germany has very high unemployment among immigrants. At the same time, they need resources, and when they age, they're going to need to be taken care of as well.

That increases the problem and puts more load on the systems that are strained to begin with. That would look totally different if it was a different group of immigrants, but we have to look at reality, not a theoretical ideal.