I was being a tad facetious with the "burn it all down" comment, yes

But the issue isn't resource allocation, it's a drop in resource
output from population decline that concerns governments and some economicists. (Plus a drop in QoL is generally assumed to lead to civil unrest, and people are dumb so that has a risk of leading to the Very Bad Things).
Using immigration to drain excess population from other countries, raising the retirement age, and making more babies are ways to maintain output (in the short-term at least), whilst reduction of the cared-for population would reduce the burden on what is being output to try and balance out the reduction from population decline*. Western countries have been relying on the former for a few decades now, but that well is drying up. The "Middle World" is joining the "below 2.1" club this decade, quite a few of them already have, and Africa is predicted to do so next decade.
By modern economics I meant the whole "globalised assumption of continued exponential growth of GDP over time". From the theorizing I've seen, population shrinkage is assumed to lead to GDP reduction, which leads to "everybody panic aaaah fire burn it down mad max time! oh wait that didn't happen? huh...oh no it's happening again aaaah!".
The potential "End of Global Economic Growth" is touted as being the next "The Bad Thing" to deal with, so Governments are trying to find ways to put that off for some future lot to deal with.
(* Also never said mandatory euthanasia, the (somewhat weird) argument I've seen from the people concerned about the "cliff edge" is that legalized voluntary euthanasia for general quality of life reasons rather than only terminal illness would be 'enough')