I have railed before against the bad practice to use Calvo pricing to represent price rigidities, and here is more support. Fang Yao demonstrates that the tractability that Calvo pricing buys is more than overtaken by the lack of proper dynamics that results from it. The point of comparison is the almost as old and antiquated Taylor wage-contract model.
Now imagine the size of the gain in realism and dynamics one would have in a model where agents would actually decide whether to change prices or not. Calvo (and Taylor) essentially assume that no matter what the circumstances, firms will patiently wait for their turn before adapting prices, even if this means they are foregoing significant profits and know it. That is silly. And we have nowadays ways to overcome the tractability issue with numerical simulations.