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All economic theories are unproven, approximations about how economists think people might behave. There’s a reason it is often referred to as the ‘dismal science’. Quite often they are based on counterfactuals and projections of what might have happened.
The Laffer Curve is not a rule which always reflects reality but it has explanatory power in certain situations, since logically there has to be a point where avoiding taxes becomes more appealing than paying them.
Regan, et al deploying the theory as part of their political rhetoric - potentially in bad faith - shouldn’t discredit the concept itself because doing so would be throwing the baby out with the bath water. It’s an ad hominen attack against an economic theory; a bit like saying capital controls are always bad because President Xi in China frequently uses them.
I think we agree about the nature of scientific enquiry, how it is all based on inductive reasoning and cannot provide the certainty of mathematics. Additionally, it looks like we agree that the Laffer Curve has been used to justify bad policy in the past.
However, I don’t think that the theory has been debunked in the way you are describing. There is broadly a difference of opinion between Keynesian economists who are skeptical of the theory and then Supply-Side economists who endorse it; and then a whole spectrum of views in the middle from Behavioural economists or other schools of thought who are more ambivalent.
Academics who do support the view have done empirical studies over the years that they believe suggest that the Laffer Curve is real, see:
It’s a matter of live debate in the field regardless of your opinion of the theory.