Saying that insight isn't useful (that you can reduce any Boolean equation to a single universal gate) - when it is a cornerstone in modern equivalence checking, Boolean SAT solving, and minimization of combinatorial equations) is really, really missing some very key things...
It is the kind of fundamental cornerstone that allows modern digital computers to even exist.
Doesn't equivalence checking normally use BDDs, and SAT solving normally use separate AND, OR, and NOT? I mean the algorithm to reduce an expression to CNF is a pretty simple set of local rewrite rules with AND, OR, and NOT; I could be wrong but I feel like the NAND-based equivalent of CNF is quite a bit hairier.
As for minimizing combinational logic, don't you want to use the full set of gates available to you in that case, taking into account their cost, and maybe trying to minimize or at least limit circuit depth? It seems like just using NAND would be kind of a step backwards in that case. Karnaugh maps give you DNF; PALs/GALs want DNF; the fact that your DNF PAL circuit might just be two layers of NAND (equivalent to a layer of AND feeding into an OR layer) is kind of an implementation detail, isn't it? I mean you would configure the circuit in the exact same way if it were made out of physical AND and OR gates.
Of course after you do the minimization, you move to a technology mapping step that takes these things into account.
"the fact that your DNF PAL circuit might just be two layers of NAND (equivalent to a layer of AND feeding into an OR layer) is kind of an implementation detail, isn't it?"
They're entirely different levels of abstraction.
https://en.wikipedia.org/wiki/Functional_completeness This line in particular: "In digital electronics terminology, the binary NAND gate and the binary NOR gate are the only binary universal logic gates."
Saying that insight isn't useful (that you can reduce any Boolean equation to a single universal gate) - when it is a cornerstone in modern equivalence checking, Boolean SAT solving, and minimization of combinatorial equations) is really, really missing some very key things...
It is the kind of fundamental cornerstone that allows modern digital computers to even exist.