It's not the most intuitive thing, but how long we live has no long term impact on population levels. Think about a fertility rate of one - this means each successive generation will be half the size of the one prior. This makes simplified population sims very simple because it's simply powers of 2.

If you start with a population of 1 then the generation before was 2, then 4, 8, 16, 32, etc. So when you remove the biggest group, the oldest, it will always be about 50% of the total population regardless of how many other generations happen to be alive. And a 'generation' is proportional not to our life expectancy, but to our practical fertility window - so about 20 years.

You would substantially mitigate many of the economic problems but your Logan's Run would also need to be a dictatorship (and a rather less than benevolent one) because the skewed age ratios mean with a collapsing fertility rate the elderly will exclusively control any democracy, even if 100% of people vote. And all of this just to make it more comfortable to sleep walk into extinction.

I'm fully on board with you about saying the unspoken parts out loud, but I don't see this idea as a solution.