A Poisson equation with all Neumann boundary conditions has a single constant dimensional null space. When solving via a Krylov method, the null space can be removed either by subtracting the mean of the solution each iteration or by pinning the value of a single vertex.
Pinning a single vertex has the benefit of simplicity, and also avoids an extra global reduction per projection. However, it is typically viewed as bad due to its effect on conditioning. Therefore, I've always subtracted means.
However, the two methods differ from each other by at most a rank 2 correction, so according to (1) they should converge in nearly the same number of iterations (at least in exact arithmetic). Is this reasoning correct, or is there an additional reason that point pinning is bad (perhaps inexact arithmetic)?