It’s indeed an interesting question how much we should care about “non-constructive” criticism. If you correctly point out a mistake in a mathematical proof, this is valuable even if you don’t offer a proof of your own. But if you’re choosing one of several theories of physics, a low posterior probability (or low observed likelihood) doesn’t give you enough reason to reject the theory: you must also find a different theory with a higher posterior, or you’re a bad Bayesian. This is one of the reasons many people don’t like Bayesianism :-)
It’s indeed an interesting question how much we should care about “non-constructive” criticism. If you correctly point out a mistake in a mathematical proof, this is valuable even if you don’t offer a proof of your own. But if you’re choosing one of several theories of physics, a low posterior probability (or low observed likelihood) doesn’t give you enough reason to reject the theory: you must also find a different theory with a higher posterior, or you’re a bad Bayesian. This is one of the reasons many people don’t like Bayesianism :-)