As to the MDA being used as a DA, Theo VanDeV at KLM clearly showed during AWO HWG deliberations over two decades, ago why this policy to set MDA=DA is safe and appropriate, without needing any 50' additives, but some states and authorities have nonetheless been slow to take advantage of the increased safety of using VNAV paths with MDA=DA, in lieu of "dive and drive", by still assessing a completely unnecessary 50' additive penalty.
"dive and drive" has nothing to do with adding 50 feet. It is irrelevant in this context because "dive and drive" is seldom used anymore. Use of a DA or MDA in this case both involve approaches along a predefined flight path angle using the aircraft vertical nav capability.
The issue of whether to add 50 feet is related to the accuracy of the approach, navigation equipment and the regulatory limitations of the operator.
A DH assumes that a decision to land or go-around will be made no later than at that height, and it is permissible for the aircraft to dip down below that height in case of a go-around because of its inertia. It is predicated on the aircraft being exactly at the MAP location, as guaranteed by the precision approach system (ILS) for example, so that adequate clearance above obstacles is maintained.
An MDA assumes a lower degree of precision, in which case the MDA is the lowest altitude the aircraft can descend, taking into consideration the highest obstacle within a certain radius of the MAP (plus the path from the FAF); the exact location of that obstacle in not considered in the approach. The typical height above this highest obstacle is 250 feet. Because of this uncertainty, the aircraft must never be allowed to descend below MDA unless visual, because of the potential but uncertain proximity to this highest obstacle. This is why 50 feet is added: to allow for the dip in altitude due to inertia and reaction time when deciding to do a go-around, assuring remaining above MDA.
RNAV approaches can either use DA or MDA, depending on the operator certification and the accuracy of the nav equipment. If you look at a GNSS approach plate, you may see 2 sets of minimums: one for LNAV/VNAV and the other LNAV only. Under the former you will find a DA and under the latter a MDA. 50 feet must be added to the MDA, unless doing a 'dive and drive' descent, which is still legal but not SOP. Some major operators in Canada are not approved for LNAV/VNAV, despite having such limits on the approach plate.