Isn't the core issue that energy use and economic growth are deeply connected? If America uses a little less thanks to a carbon tax, it will just be cheaper for india and china, and their prosperity will grow more while americas begins to lag?
That's only true up to a point (see: efficiency, the length of logistics chains & so on). For the remainder, GHG footprint only holds for fossil-dependent economies.
Move to renewables & you're literally decoupling energy use from GHG emissions.