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One obvious issue with the Laffer curve: Nobody actually knows where the peak is.

No, but that doesn't mean it isn't there.

Most social sciences (including economics) can't very well be exact for the lack of experiments, much less controlled experiments.

If you don't know where the peak is, you can't argue that raising taxes will reduce GDP because you don't know if you're going up the hill or down it.

And that's fine, because that's not the purpose. The purpose is to argue that the relationship isn't linear (as might be intuitively expected), but curved (I don't know what the shape is called).

It's impossible to accurately model the economy of a society, but theories like this can help politicians better judge the impact of their policies.

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