Consider the German family name Schmidt, Schmid, Schmied, Schmitt, Schmit, Smid, Smidt, Schmitz, Schmidl, Schmidli and Schmidtke, all derived from the profession of smith. If a descendant of every one of these variations decides their spelling is the correct one for their family and therefore applies it retroactively to their ancestors we could theoretically end up with 11 duplicates of the same person and a good number of his descendants. That gets even more complicated when the family lived in a bi- or multilingual environment where records were sometimes kept in either of the languages in question or in Latin. There are related families from the former Bohemia, for example Ohnheiser and Nechodomu (meaning "Without a house"), or Wölfl and Vlček ("little wolf"), where the recognition of duplicates would be even harder.
Clearly, we need a standard to go by, and a primary source, preferably a birth or baptismal record, lends itself for this purpose. We have the "preferred Name" field and "Current Last Name" field to record the common usage.
As to using names in their declensed forms would only occur to native speakers of languages that don't do that. For the many languages that do use declension of names it would only be natural to use the nominative of a name found in the genitive form - unless it has become a patronymic and then developed into a family name such as Bernhardi - [son] of Bernhard.