You are correct that pointing out a logical fallacy does not necessarily address the claim itself. However, using faulty reasoning to justify a claim is an important thing to point out. It undermines the validity of the claim itself. Furthermore, excessive display of faulty logic prevents being able to follow conclusions from the evidence presented, or connect whether the evidence supports the conclusion or undermines it. So it is usually important to identify faulty reasoning if only to help prevent the recurrent pattern of known sources of error in argumentation and drawing of conclusions.

That said, once the underlying logical fallacies are addressed and the ramifications sorted out, the claim itself then needs to be evaluated if there is any merit to it left.