Would it, though? What matters is glycemic index, and that depends on the overall composition of the food, not just on levels of simple carbohydrates. Focusing purely on one nutrient or on total caloric content is hopelessly reductionist.
For instance white bread has a high glycemic index not because of added sugar, but because all of the fibre and most of the protein have been removed. Proper whole grain, brown bread has a low glycemic index and tons of protein. And that's true even if there's some syrup added for flavour, which is not uncommon.
I believe sugar is added to sliced bread primarily as a preservative and to retain moisture. When fresh I've never noticed much of a difference between "no sugar added" and comparable sliced bread with corn syrup or honey, but the former goes stale more quickly.
The economic pressures are at odds because as people eat less bread shelf stability, both at the grocery store and at home, becomes increasingly important to maintaining a desirable yet competitively priced product. People don't want added sugar and are more carb conscious generally, but what they dislike even more, without realizing it, is stale bread. So you get a positive feedback loop that turns people off of bread, I think.
For instance white bread has a high glycemic index not because of added sugar, but because all of the fibre and most of the protein have been removed. Proper whole grain, brown bread has a low glycemic index and tons of protein. And that's true even if there's some syrup added for flavour, which is not uncommon.