Doping usually increases defect density in the material. Grain size is also influenced. Also doping severely changes the electrical and electronic properties of the material. So, bandgap tuning without doping could be useful.
However, doping is an easy and cheap way to do so. That's why band engineering with doping is pretty common.
Band gap engineering is usually performed by controlling the semiconductor alloy composition ratio (e.g., AlGaAs). The compound materials are hence highly doped materials (x is in the order of 0.1 to 0.9). This is well done in absence of other doping materials.