You’ll need to kill people off at say 70. Healthcare meds increase dramatically when you get older and older, and that means more people needed to care. When the worker:dependence ratio increases you end up with people emigrating or care reducing.
In your solution you also wouldn't have to kill people off. They would die naturally due to a lack of healthcare.
As for the why: because historically that has always been a solution to lacking specialized talent or simply not having enough hands to perform a massive task. You don't want to pay domestic labor, so bring in foreign labor. This time it's a general problem.