A new thought about free will

I get a bit tired of the Youtube "free will doesn't exist" discourse, but I did happen to watch some of an Alex O'Connor video about it this morning, and read some of the comments.  One of them made a point that I don't remember thinking about before:   even if free will exists, it's not provable. 

My reaction: makes arguing about its reality a bit pointless?   Although you can still argue usefully about the merits of assuming it exists, or doesn't exist - and really it is that practical aspect of it that does bother me more.  And shouldn't the "no free will" side also be a bit humbled too?   They, being very sciencey and all, are presumably fine with Godel showing that there are true things that are unproveable in maths, so they should accept that free will might be true too?      Be more like an agnostic about it, and not like an atheist?   (It's not like the sense of free will is something invented, either: just because the Flying Spaghetti Monster doesn't deserve belief just because it is unprovable doesn't mean that it is a good analogy to belief in something of which people have a first hand sense.) 

Anyway, these are the arguments that Gemini gives in support of it being unproveable:

The Core Arguments for Unprovability

• The Observation Problem (Distinguishing Determination vs. Indetermination vs. Agency):
  To prove free will, you would have to show that a human decision was caused neither by prior physical states (determinism) nor by pure randomness (indeterminism), but by a genuine, unconstrained "self" or non-physical agent. Science can only ever measure events as either correlated/caused or stochastic (random). An empirical test cannot capture or isolate an uncaused mental cause without it looking identical to randomness from the outside. [1, 2]
• The Infinite Regress of Will:
  Even if you feel you made a choice, you can always ask: Did you choose what you wanted to want? If you trace any decision back, it rests on desires, values, and neurological states that you did not author. Proving that the ultimate locus of a choice resides in a free self hits an untestable regress. [1, 2]
• Subjective Experience vs. Objective Verification:
  Free will (in the libertarian sense) is experienced purely from the inside as first-person phenomenology. Science relies on third-person, reproducible, objective data. Because subjective states cannot be directly translated into an objective proof that bypasses physical laws or random chance, the claim sits outside the boundaries of empirical verification.
• The Observational Equivalence Problem:
  A universe with free will and a deterministic universe (or a compatibilist universe) can look behaviorally identical. If every choice a person makes can be interpreted as either "freely chosen" or "the inevitable result of prior brain chemistry and environment," the data is underdetermined. No experiment can slice cleanly between them. [1]