The A320 and A330 family are FBW aircraft that use C* longitudinal control laws for longitudinal sidestick command tracking. In essence, stick neutral commands 1G flight. When stick is deflected longitudinally, a blend of pitch rate and normal load factor is commanded to provide a consistent G-feel to the pilot; once the stick is released, 1G flight resumes, but the airplane is steady-state at the new pitch angle (or flight path angle to be more exact).
Unlike B777, B787 and A220, however, the A320/330 family do not have artificial speed stability. Once the aircraft is steady-state at the new pitch attitude, and with the autothrottle disengaged, the airspeed will settle to a new trim point. In another word, unlike a conventional aircraft, the A320/330 only has neutral speed stability.
This is why the envelope protections of the Airbus aircraft are not nice-to-have features, but essential features to ensure the airspeed does not rapidly bleed off to stall or increase to overspeed, all while the stick is neutral.
My question is, why is a C* control law without speed stability desirable for a transport category aircraft? The A320 does not need to perform precision target tracking as a fighter aircraft would, and it changes the flying characteristics drastically from those of a conventional aircraft.