"Intuitive" does not necessarily imply "true." Some of the most pernicious false ideas are ones that have an intuitive appeal (especially in an oversimple example scenario).
The Laffer curve likely falls into something like that category. If it has any truth to it, it's in conditions that don't actually exist (like an effective 90% tax rate).
It (and “supply-side economics” in general) is not a serious economic theory.
Well, also the usual one-dimensional presentation of the tax-policy space that goes with the curve, but that's not so much contentious as obviously wrong.
The people who think it is important tend to have a religious faith that the status quo is in a space where decrease of taxes in any aspect of tax policy moves is back toward the maximum, which, even if you accept the existence of the Laffer Curve, is a claim which needs a lot of justification which is never offered.