Well yeah, the sugar is also there to produce the soft squishy texture people expect from sandwich bread as well as the aiding the Maillard reaction when it's grilled. Miss me with a grilled cheese made with any other kind of loaf.

But we are talking about bread here, even in the absence of sugar and oil it's still got plenty of calories for you. Grain St Methode's white bread, a no added sugar brand is 180 cals for two slices and Wonder Bread, famously packed with sugar, is 140 cals for two slices. It's the bread which is making you fat, the sugar isn't moving the needle in any direction as far as the obesity crisis is concerned.