To remove the case type do the following (1) Use the Refactoring Rules -> Delete a Class (From Designer Studio | System | Tools) to delete the class associated with the case type and (2) Refresh the case types listed in the Case Designer.
I would not do this in a production system or if any instances of the type had already been created. Also be very careful if the case type has any subcases.
Ok sure. So let's say you have an existing case instance that covers a claim for $1,000,000 USD, and it is still open. Then the case type for that instance gets deleted. Then the customer service representative tries to finish the processing of the claim. It isn't going to work, and the customer won't get paid without manual intervention.