Are all databases reducible to this ultimate abstract database design?
This insight was made at least as far back as 1886, by Alfred Kempe.  In fact, he observed that any set of relationships (not just those that are already relations) can be captured as a binary relation.  At the time this seems to have come as a shock to Charles Sanders Peirce, who had built his relation algebra on the idea that any relation can be captured by means of ternary relations, and who up to this time apparently believed this to be the best possible.  Kempe used graphs to illustrate his notion, while Peirce used edge-labelled graphs.  In a long and admiring review Peirce revised his theories to accommodate binary relations as a possible foundation, and distinguished the two approaches:


  Mr. Kempe's conception depends upon considering the diagram purely in its self-contained relations, the idea of its representing anything being altogether left out of view; while my doctrine depends upon considering how the diagram is to be connected with nature.


In terms of modern database representations, RDF corresponds to Peirce's ternary relations, while key-value stores correspond to Kempe's graphs.  As Raphael pointed out in a comment, these are essentially the ideas behind graph databases.

As an aside, the arguments about binary/ternary/quaternary/quinternary/... tuples being the "best" foundation for data representation still rage on in the W3C semantic web working groups.  I believe that the original insight of the relational model was that for efficiency, one should use relations of the right arity; relationships that are naturally represented as tuples should not be transmogrified into more complicated data structures just for reasons of purity.  However, this argument also goes the other way: relationships where different instances naturally have different arities should not be shoehorned into a rigid relational schema just to preserve the purity of the data model.


A. B. Kempe, A Memoir on the Theory of Mathematical Form, Philosophical Transactions of the Royal Society of London 177, 1886, 1–70.
C. S. Peirce, The Critic of Arguments (1892 essay), in Collected Papers of Charles Sanders Peirce, Vol. III, Harvard University Press, 1933, 250–265.