Polymorphism is more complex than a switch/case in a single instance. Across a large codebase using polymorphism instead of hundreds of different switch/cases is simpler, especially when you need to change something. Encapsulating what a class should do within the class instead of in an external code block is much simpler when you're working on something big.
Polymorphism is a switch, but it is the switch over object kind, not action. In fact if there are only few subclasses compilers for some languages where a global analysis is possible implement polymorphic calls as switches over the object tag.
And notice how if one needs to add a new action, all objects are required to implement it. In typical OOP languages that touches many files even if the action is used only once.
So polymorphism works nicely if there are only few actions but many different objects, like in a typical GUI. But in cases of few objects and many actions, for example, doing a lot of different queries over few data sets it leads to a lot of boilerplate. Switch over actions will lead to less code.
