Except the history of such proofs suggests we not take them too seriously, because they necessarily depend on assumptions that may or may not apply to our universe. Hawking's proof that our universe contains a singularity in its past depended on a positive pressure assumption that is violated in inflationary universes but that was believed to be compellingly reasonable at the time, for example.
The important thing is that our inability to imagine a universe that violates some assumption tells us nothing about the likelihood that the universe violates it. What we can or cannot imagine is simply irrelevant to the way the universe actually is. No one could imagine a universe in which anything like Bell's Inequalities could be used to test local causality until Bell derived them.
There was nearly 200 years of philosophy arguing that no such test could possibly exist, culminating with the positivists just decades before it was found, and 2000 years of philosophy before that arguing that no such universe as one in which Bell's Inequalities were violated could exist, because no one could imagine such a universe, or such a test.
This is why science and math are different disciplines. Science is the discipline of publicly testing ideas by systematic observation, controlled experiment and Bayesian inference (if you read that definition carefully you'll find it's a lot closer to "Anything goes" than Popperian hypothetico deduction). Math is the discipline of formal deduction from axiomatic premises, or something like that. Math is an incredibly useful tool in science, but so is plumbing.
The attempt to prove there is one consistent theory of the universe is ambitious and interesting, but there are good reasons many scientists are skeptical about it. It has resulted in a great deal of interesting math and no strongly testable predictions over the past century (string theory encompasses so many diverse models of the low energy world that its predictions only ever knock off models, not the family of theories proper).
Testable predictions come in many forms, and "unique consistency" is one of them. It's just not one that many people outside the string community think they can achieve, and my personal bet is that the next century of string theory will involve a widely-believed claim that the uniquely consistent theory has been found, followed by its collapse some time later as a key assumption is found not to be true of the universe it is supposed to describe (that is if loop quantum gravity doesn't take the field on an experimental basis first.)