Price rigidity all wrong

Much of macroeconomics, and in particular New Keynesian Macroeconomics keeps relying on price rigidities to get anything monetary to have any relevance. That is not necessarily bad, but it becomes problematic when this is implemented with Calvo pricing which essentially states that no matter what the state of the economy or how long ago a firm has last changed its prices, firm change their prices with the same probability. This is an utterly ridiculous assumption against which I have already railed often, but people keep using it because it is analytically convenient. I am still looking for a good model of price rigidity, beyond the ones already discussed here. (Previous posts: I, II, III, IV)

The latest candidate is by Paul Middleditch. When I saw the title, A New Keynesian Model with Heterogeneous Price Setting, I was very hopeful to finally see a NK model where firms are heterogeneous and decide when and how much to change prices, leading to fluctuating proportions of price changing firms. My hopes were quickly dashed. The heterogeneity here is simply that there are three types of firms, each blindly obeying to a different Calvo probability. Nothing to see here.