Keep in mind that immigration is actually a small part of this; the much much more important element is birth rates. The core issue in the US is that we made promises based on an economy where the baby boom generation was working to support their parents in retirement, but we're going to need to pay up in an economy where millennials are working to support the baby boom generation in retirement.
> A more robust, sustainable solution is to improve productivity via other means (including automation).
Sure, that would be nice. It's also completely impossible. Productivity growth has never, ever, ever grown fast enough to bail us out of the hole we're in now, and we have zero (repeat, zero) ideas on how we could possibly change that.
Productivity growth will not save us.