Well, to your first point, I'd say that productivity in relative terms is a more useful measure in this case because that's generally where the best investments are to made - if we're sticking with the "investors don't need america" part.
The issue with using absolute productivity in a global world is that comparative advantage in production (i.e. higher productivity growth, and with it higher real incomes in the developing world) are the driver for lifestyle.
Think of it this way: if others are wealthier, they'll put upward price pressure on supply side of goods that American's buy (look at copper for example) - while at the same time American productivity (vis-a-vis real income) decreases (or at least remains flat) make these goods less affordable from the demand side.
This means lifestyle, even with a fixed absolute productiviy, will decrease.
The issue with using absolute productivity in a global world is that comparative advantage in production (i.e. higher productivity growth, and with it higher real incomes in the developing world) are the driver for lifestyle.
Think of it this way: if others are wealthier, they'll put upward price pressure on supply side of goods that American's buy (look at copper for example) - while at the same time American productivity (vis-a-vis real income) decreases (or at least remains flat) make these goods less affordable from the demand side.
This means lifestyle, even with a fixed absolute productiviy, will decrease.