The data/facts disagree with you. In a low birth rate society a constant influx of new tax payers is required. Without it you end up with decades of stagnation like Japan.
1) Populations are their most expensive at their oldest age and each subsequent generation is smaller and needs to pay for an old generation larger than their own
2) infrastructure and many of the things a government provides is not scalable down and up. A road is not (much) cheaper to maintain because less people drive on it
This sounds like a strong argument for having a stable cap. It's not a total immigration ban and would freeze population at a steady state. This makes all of the boom and bust problems easier, not worse