The P vs NP problem is open. How about the following questions--Can SAT be done in $n^k$ time for some specific $k$?

Why do I ask these questions? Ben-David and Halevi's paper On the independence of P versus NP proves that if P = NP is independent of PA, then SAT can be solved in $n^{g(n)}$ time, where $g$ is a very slow, almost constant function. This means that if we can neither prove nor disprove SAT is in P, then SAT lies on the boundary of P. It's not in P and it's not outside P either. So there's a gray area near the boundary of P. Because of this possibility, I think the P vs NP problem is not a good formulation. I therefore propose to ask more precise questions like whether SAT can be solved in linear/quadratic/cubic/etc time.