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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.
ok, so scientifically speaking "proof" is a mathematical concept only, physics doesn't prove shit, chemistry doesn't prove shit, no other science proves shit.
But economics, like every other science out there makes models, these models when applied to certain circumstances make predictions, we test these models by testing the predictions they make.
The more accurate the prediction the better and more relevant the model, the issue that economics has is that many people instead of looking at the actual science, take the fictional work and claim it reality, mainly because they believe some propaganda commissioned by really wealthy people, to keep their wealth. the Laffer curve is one such example because it allows rich people to invest into lower taxes and increased privatization.
The Laffer curve isn't bad because Regan used it, it's bad because it has a track record of not having any predictive capability.
Also, there exist mechanisms by what we punish tax evasion, taking the likelihood of tax evasion into account for the purpose of setting tax rates is self-defeating, in the assumption that any persons want the maximum amount of money for themselves would always try to evade taxes, no mater what the tax rate is.
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.
sure, you have listed a few papers, and having skimmed some of them I'm a bit iffy to their relevance mainly as to what numbers they take as indicators what of and at least one had an issue where one of the more prominent indicators they picked is heavily influenced by other outside activity more so than the taxes.
but here's the thing, if it was just wrong all the time, it would have predictive power, the fact that it sometimes seems to be correct, and other times it being counter to predictions or being mostly non changing means that it's not a useful model, and a useless model is trash, and honestly I'm highly skeptical of supply side economics, it has produced relatively little in terms of economic stability, nor sustainability.
personally, I'm more inclined towards Post-Keynesian demand side economics, and unlike supply side economics, they have actually made predictive models that actually have predictive power