The difference is not great between "The cause and reason ought to be assigned to each thing why or why not..." and "The cause and reason of each thing why or why not... ought to be assigned..." Though the Genitive after causa is more literal.
I think the most significant reason for choosing the Genitive rather than the dative is continuity. The formula "each one of the...ought" helps the reader to see how the argument develops:
PROPOSITIO X: Unumquodque unius substantiæ attributum...debet.
'each several attribute of a single substance...ought.'
This is followed (in the middle of Proposition XI) with
... infinitis attributis quorum unumquodque...necessario...
'with infinite attributes each one of which...by necessity...'
So, in the first horn of the dilemma
ALITER: Cujuscunque rei assignari debet causa seu ratio
'IN THE ONE CASE: The causa or ratio of each res ought to be attributed...