"Don't think of it as dying, think of it as beating the rush."

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.