It's interesting that a single formula "encapsulates" all of Boolean logic, but I fail to see why having a single formula, rather than two or three, makes thing

It's interesting that a single formula "encapsulates" all of Boolean logic, but I fail to see why having a single formula, rather than two or three, makes things simpler rather than more complex. The proposed formula with 6 NANDs is almost impossible to intuitively understand. Why give up axioms that are easier to understand, like the Peano axioms, or even the pair of 4-NAND and commutativity axioms, just because you want one formula? I do see some value in it, but the idea of "simpleness" being captured by "least number of formulas" seems shortsighted.