Too much population ageing is not a good thing, and if you don't address low child birth rates in some way, then you'll have a society with too many old age people, and not enough younger, working age people. The economy will suffer, and it will take a toll on older folks who rely on younger people pouring money into the social structure which pays our their retirement checks. Statistics say that immigrants, who tend to be younger, not only start businesses at a higher rate, but also tend to have higher child birth rates than natives of the countries they go to. There has been tons of research on this, might be a good idea to read up on it.
Anything out of balance and not addressed eventually becomes a problem, just like eating too much or drinking too much. You wouldn't want too much population ageing... or too much immigration. The key is balance, i.e. controlled immigration.