I love how you distinguish between "ICs" "Management" and "Product". When you say "Product" do you mean Marketing? Sales? Production? Manufacturing? Do they have "ICs" as well as their own "Management"?

The whole point of "Agile" was supposed to break down these divisions. Management is "generally charged" with getting the greatest productivity they can out of their resources. How that productivity is measured may be by "the priorities as set by Product", but that doesn't take into account ROI, sunk costs, COGS, Cap/Opex etc etc.