There is no “zero” immigration policy, this is a strawman. Controlled immigration is different from opening the floodgates. Also weird to admit that no country has reversed its birth rate problem, but still insist upon massive immigration being the solution.
America has, it reversed below subsistence rate birth rates. More importantly despite some years of negative population growth the net long term trend is slow population growth.
So despite both issues the long term trend is slow net population growth. Thus significantly below subsistence birth rates where flipped from a massive issue to a non issue.