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.
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
Why shouldn’t the need for tax revenue go down as the population it’s intended to serve declines?