the classical view of concepts if false

If it is, it doesn't seem to me to be false by virtue of not corresponding to how the brain stores concepts. The notion of knowledge as justified true belief can be rejected by appealing to examples that (as far as I can tell) you could come up with even in ignorance of modern cognitive science in general, and typicality effects in particular.

You can reject the proposition "concepts are represented in the human brain in terms of necessary and sufficient conditions" without necessarily rejecting the proposition "it is useful to talk about concepts in terms of necessary and sufficient conditions". You've shown convincing reasons to reject the first proposition, and you've shown some counterexamples to the second proposition, but you also seem to be implying that if we accept the first then the second never holds, and that can't be right.

In fact, it is useful in some cases to talk about concepts in terms of necessary and sufficient conditions (for instance mathematical concepts tend to have this structure).

The examples you give (of typicality effects and so on) are examples of concrete, everyday concepts (bird, fruit, fish, furniture), when really the argument you want to make against the classical view of concepts is about much more abstract concepts (knowledge, truth, justice).

I don't think I understand what you're saying with the musical instruments example.

Maybe that doesn't really make sense. Allow me to retract that.