I fear that this question is premised upon a naïve idealisation of science.
Science does not prove anything, except the falsety of its own theories. And no, this isn't a bug, nor it should not do anything different. What we call "truth" is always provisional, no one can be in direct contact with the Kantian "thing in itself", everything is mediated by our perceptions, which are not the "true thing".
Why would linguistics be different from particle physics? Both languages and subatomic particles are part of "reality", and can be discussed, labeled, theorised, spoken about. There is a scientific method - propose a theory, isolate variables, design an experiment, perform the experiment, compare the experiment's result with the theory's predictions. This is no different in linguistics than in any other science.
If linguistic theories are in any sence worse than subatomic physics theories, this is a problem of the relative development of each science. Yes, physics as a whole is more developed than linguistics, due to both historical (scientific linguistic is newer than scientific physics) and structural (recursivity in linguistics is more immediate than in physics) factors. But then physics was a mess two centuries ago, too.
Physicists disagree on a lot of things too. Which is a good thing; how would physics ever progress if physicists adhered to previous results as dogma? We would still believe in epicycles, I suppose.