15 degree pitch limits were a standard on older aircraft. Original DC-9 and B727 series and other aircraft of that generation limited pitch to 15 degrees because the air data systems were not as capable, nor designed to program a flight director with real time data in the event of an engine failure.
Limiting pitch to 15 degrees on the old B737-100 with dash 15 engines meant that the aircraft would accelerate during climb but if was felt that 15 degrees would satisfy the requirement for control ability in the event of an engine failure.
The MD-80, first delivered in the early 1980s, had a flight director / air data system that was programmed for good pitch data in the event of an engine failure. It would give pitch commands to maintain V2+10 and no less than V2. A V2 cut in a Mad Dog is a real chore and requires a both hands on the yoke push to the pitch bar while keeping the wings level. Engineers at McDonald also admitted that one of the reasons for the pitch commands going to V2+10 was for noise abatement.
One way to reduce the noise footprint was to program the flight director to get the maximum altitude possible as quickly as possible. When measuring noise in a standardized manner, for certification purposes, if all things are equal, the aircraft with the higher altitude will register less noise than the same aircraft under the same conditions at a lower altitude.
To get back on point, the A320 is limited in pitch, with hydraulic failures, to allow the pilot sufficient control to quickly maintain the required lower pitch in the event of an engine failure. Pitch authority is limited given the conditions shown by the original poster.