DAs/DHs aren't normally increased due to obstacles that occur on final approach prior to system minima as any such obstacle would probably demand an increased GP angle. Increased DAs/DHs are far more common due to problems in the missed approach segment which for a precision approach commences at system minima, i.e. the 200ft/0.65nm point.
Maybe I am not correctly understanding this statement, but ... the TERPS criteria allow relatively little change in GP angle in most cases. More likely that the DA would be increased as needed to assure required obstacle clearance and stay close to a 3 deg GP angle. Agree on the MA segment. One reason for increased DA is to meet the standard minimum climb gradient on the MA segment. Some airports have multiple precision approaches to the same runway with different DA's depending on the climb gradient the acft is capable of.