All other things being equal, and assuming the heat treat increases the material strength. What actually happens in most cases is that manufacturers exploit a higher strength alloy composition or temper to reduce the amount of material, as everybody likes light weight bars until they break.
No, and if they just increased the material strength without altering the geometry, your point stands for their product. It's just not how the mainstream bicycle industry works.
All other things being equal, and assuming the heat treat increases the material strength. What actually happens in most cases is that manufacturers exploit a higher strength alloy composition or temper to reduce the amount of material, as everybody likes light weight bars until they break.