It's doable, we already had societies that deployed such restrictions on a scale similar to the global human population. Whether it should be done is another question, as many people criticize the issue of the state policing procreation.

That may be particularly true for billionaires, who profit off of a growth engine that is going to be under serious pressure once the population starts dropping for real. Increasing life span (in particular increasing the span of life not dominated by illness) could balance out quite a bit of declining fertility rate. And I for one think that if fertility became more dominated the people who want to be fertile, it would be a Good Thing.

I'm not going to worry about immortality, because I think it's still very very far out. Which means your trillionaires are about generational wealth. Generational wealth is lost by the first generation 70% of the time, by the second 90% of the time. It's not that big of a thing.

I'm just not too worried that 110 years of healthy life is going to tip the balance too far. It'll slow down progress some ("X advances one funeral at a time"), and we'll massively screw things up for a while, but long term it seems good to me.