Look at the two examples where k is used with β being a String or a List. And now combine the two examples, this would force β to be simultaneously String and List -- impossible. A type parameter is not what we want here.

The return type of the continuation is better captured by something like the Bottom type from Haskell:

https://wiki.haskell.org/Bottom

In particular, "Bottom is a member of any type", which is what solves my example above.