If one follows the notional glidepath that the designer envisaged when drawing that particular 2D approach (i.e. by following the altitudes v distance to go as depicted on the plate), one should arrive at DA (MDA) before the MAPt. In this case, initiating a MAP at DA hence "ducking under" DA (MDA) as the aircraft transitions from a descent to a climb, would probably permit adequate terrain separation (OEI) during the missed approach segment.
If, on the other hand, one was less than diligent in following the notional glidepath, and arrival at DA (MDA) coincided with the MAPt, it is clear that one would now be following a path on the missed approach segment that was below the designed path. Terrain separation is now not assured. This therefore would have to be taken into account when deciding when to initiate the missed approach procedure i.e. earlier than DA (MDA).
There has been no redesign of the 2D approach in order to derive a DA. The procedure design is based on MDA. For example, the OCA for the NDB/DME RWY 27 approach at EGBJ was 600 ft in July 2005. The DA (MDA) today is also 600 ft.
I would have thought it unwise to brief different minima depending upon how close to the MAPt one may end up at DA (MDA), hence our company DA is published CDFA DA + 30 ft.