The true answer to the question is as simple as it is subtle.
The A320 balloons at the selection of Flap 2, WHEN THE AUTOPLIOT IS ENGAGED. The autopilot pitch authority is soft by design and will never pitch forward fast enough to prevent ballooning. Has nothing to do with trim software, trim is to relieve aerodynamic load, not change pitch.
When hand flying, the aircraft will not balloon because we as competant pilots ANTICIPATE and pitch forward to prevent the balloon.
Airbus have not been able to design software that can anticipate. In all situations computers are reactive only.
Why does the A320 not balloon at G/S*? Because by design the autopilot pitch authority is increased in G/S* and G/S modes. The increase is necessary to hunt the G/S acurately.
Why is the A320 less likely to overspeed or underspeed in EXP mode? For the same reason, by design autopilot pitch authority in increased in EXP CLB and EXP DES.
Where is any of this written? Nowhere do airbus devolve such secrets, but test it for yourself, you will find it to be true.
Cheers