I suspect you may well be right but for different reasons: Societies have a life-cycle and there are quite a few of them that feel like they've passed their Zenith and are on the way down. I don't see how that can be reversed once it gains momentum and given the upside-down cost structure that we'll end up with collapse may be rather faster than how long it took to go up.
Immigration is just a shell game in this respect, though it may postpone the inevitable for a bit. Outsourcing manufacturing, food production and quite a few other critical components for a functioning society may yield short term gains but long term it isn't sustainable and the current perfect storm of war, climate change, covid and politics may well set off the avalanche.
Countries get richer, people move to small apartments in cities, birth rate drop below replacement.
Japan, China, Europe, Russia.
The US are less bad, people want to go there and the birth rate is not as bad (more suburbia?)
We are headed toward very different times with degrowth all over and a lot of infrastructure to maintain.
Here (Canada) ’we are hiring’ signs are everywhere a lot of places will close soon for lack of workers. Then the government funds will dry up (less income tax) at the moment they need it the most to support the aging population.
Japan is just a bit ahead of the rest of us.