However, if you already have a class type for each key
I think that's precisely what I was trying to say - polymorphism makes sense when you already have a bunch of classes to do it with, and classes which already contain lots of other fields and methods; it doesn't make sense to create a bunch of classes just to use polymorphism.
Often, though, a series of complicated if statements is hinting at a type system for your objects that hasn't yet materialized in your code. I find it's a good idea to always look at cascading if statements and switch statements and ask, "Would this be cleaner if I reified these concepts as types?"
This is the single most important trick for factoring out shitty code. I cannot believe how many times reification collapsed complexity in our code base, or how not using it was the source of bugs.
If you have cascading ifs, there is a good chance there is a huge set of ifs for every place this type system is missing. Meaning, if you wanted to add another "case" to a feature, you are modifying cascading ifs in 5-10 places, not even just one.
Wrapping up all of this code into an implementation of an interface, that is "hooked in" at each contact point allows you to add a cohesive new use case by generating a new implementation of an interface, instead of "forgetting 2 places in the code" and causing massive bugs or issues because of it.
I think that's precisely what I was trying to say - polymorphism makes sense when you already have a bunch of classes to do it with, and classes which already contain lots of other fields and methods; it doesn't make sense to create a bunch of classes just to use polymorphism.