If one doesn't "complain", then that is seen as demonstrating that things are perfectly all right just the way they are, which makes it pretty darned hard to motivate change.
I'd suggest that the supposed counterproductivity is measured by those who have a vested interest in maintaining the status quo.
Your second point is important and needs to be taken into account in thinking about this, I think. I've seen how people who point out inequality, for example, are often described as whiners by those who benefit from that inequality (a certain presidential candidate comes to mind).
But, but, in my daily life, most of the complainers I run across are people who have no interest in changing the way things are. A good test -- I ask them, "What will you/we do about it?" and if they get pissed off, then yeah, they're Bad Complainers. Or if they suggest that the required change has to come entirely from someone else...