Suppose P != NP.
We know that we can make easy instances of 3-SAT at any time. We can also generate what we believe to be hard instances (because our algorithms can't solve them quickly). Is there anything preventing the set of hard instances, from being arbitrarily small, so long as for any given instance size (n) there are only Poly(n) (or even constant) instances of size Poly(n) or smaller?
For any hard 3-SAT instance, we would have to add the set of all 3-SAT instances it reduces to via looping through the NP-Completeness reduction cycle, but I don't foresee this adding to the number of hard instances very much.
In this world, we could construct an algorithm that polynomially solves all NP complete problems, except an exceptional few.
Edit: A softer variant of the question: even if we showed P!=NP, how could we know whether a given method to generate size n 3-SAT problems actually generated hard one with some requisite probability? If there's no way to know from P!=NP alone, what is required to show that we can generate a hard NP-complete problem?