Predicting the future.
If I assume conventional wisdom is always to some degree flawed, then I wonder about the wisdom of population replacement immigration. What is usually stated when the matter is addressed is that the overall population is aging and that some percentage will soon be over some arbitrary age and therefore a crisis is developing. First of all let me say that whatever the numbers there is the fact of mortality that needs to be considered. Those old folks will pass on and after they do the society will adapt to the new circumstances and no doubt continue on. The problem is the discontinuity. For a period of time a cluster of old people will stress out society. After they're gone the slow decrease of population will not be all that noticable. This is assuming that there will be a permanent birth rate of less than 2.1 per woman. I wouldn't bet on that eventuality. The crash in population as well as the previous boon in population were singularities. Technology produced one and urbanization produced the other.
It's instructive to look a a society which is dealing successfully with a population crash. That would be Japan. From what I've seen the Japanese are aware of the problem and are dealing with it. Intelligent toilets now monitor the health of the elderly, eliminating the need of additional medical personnel. Rice-planting robots reduce the need for field labor. And of course pet robot dogs show every sign of solving the companionship needs of the old and infirm. The Japanese seem to intuit correctly that there is no really good reason that the home islands should have 125,000,000 people and that if it all crashed down to 60,000,000 it would still be Japan. The only differance would be the the infrastructure would be still built out for a population of 125,000,000. The uncrowded roads extra housing, etc. would provide a built in redundancy for the entire culture. I don't really see a downside.