Your points are well taken, but they require thinking about the problem of wage setting in the markets of the real economy. New Keynesians think about the problem within their models. The models are specified to generate sub-optimal equilibria under sticky-wage assumptions. The justification they give for this method is that the phenomenon of an “under performing” economy is experienced in the real world. If their explanation seems fishy to you, then go to the head of the class.
On the reasons for sticky wages in the real world, take a look at Joe Salerno’s blog post: