BTW, it actually isn't hard at all to achieve 0 angle of attack. Airplanes just aren't held at that pitch for very long, usually. But some of them very often do go past it on the way to an AOA that the pilot needs for his maneuvering.

There aren't too many reasons to pitch an airplane to fly at zero AOA. The problem with actually using that AOA for any positive benefit is because most airplanes are designed the way they are. Most airplanes are designed with cruise as the primary criteria of their design. That usually biases the layout to have the least drag at whatever that cruise speed is. So the designers layout the wing to the fuselage, the incidence of the wing, so that at the cruise speed desired, the wing will fly at the best AOA for that speed with the expected load, and the fuselage will be at the best angle of attack for reduced drag. So the AOI is not at the zero lift angle when the fuselage is at it's least draggy angle. So if for whatever reason you then try to fly the airplane at the zero lift angle of the wing, the fuselage winds up not being at it's best angle of attack for reduced drag........ so...........

About the only reason that stands out in my mind for wanting to fly an airplane at zero AOA (a fighter plane in WWII wanting to dive away from an engagement) would be that you're looking for the fastest dive. You don't want lift out of the wing. And you want the least drag from the whole airplane. Yet that might not happen since the fuselage probably is holding back the max speed.