Immigration or Birth Rate?

I have been asked what is wrong with letting the birthrate drop in a society, therefore having to fill its needs with immigration. My usual response is look at the EU and its problems, which are worsening each year. Here is an article from the London Times regarding Catholics in United Kingdom which illustrates the effects.

My point is not that any of this is necessarily bad, but only to illustrate the society will stay much more stable with the appropriate birth rate, and controlled immigration!