Our universe has climbed mount improbable. We are improbable. We are humans, and we have our own particular conception of intelligence, which we seem to crown as the pinnacle of existence. We have done this for thousands of years in various forms (god-mind as archetype of humans, for example). AI theorists create AGI, artificial general intelligence. We can't think of anything better than general intelligence. We can't think of any other "mount improbables", and we think of our own universe in terms of objects and probabilities. So when we find that our universe is apparently fine-tuned for our existence, we look for something quantitative and outside of our own universe. It doesn't produce very many constructive results, but it satisfies us to explain away information that we can't thoroughly explain.
My idea is not that there is no multiverse. I sometimes find it difficult to imagine the non-existence of a multiverse. My idea is that without quite direct evidence, multiverse theories can be a way to explain away information, which is a lot easier than coming up with constructive ideas. Needless to say, this is different from saying that there is no multiverse.
For multiverse theories, I think the de facto standards of empirical warrant have been set too low in some cases. In many cases, people simply assign high prior probability to the existence of a multiverse. Maybe there are some other very strange possibilities which could explain the apparent fine-tuning of the universe. Multiverse theory generally entails that the observed apparent fine-tuning of the universe can be explained by an observation selection effect (maybe there is a multiverse, intelligent observers are quite complex and improbable, so it is quite typical that us human observers observe a finely-tuned universe). Could we introduce a new theory, MultiExplanation, which entails that the observed necessity of a multiverse theory can be explained by an observation selection effect (that our fishing vessel named "Science" has a net quite likely to catch multiverse theories, due to the popularity of bayesian reasoning)? This is controversial because scientists don't like to be psychoanalyzed. Generally scientists are a lot more logical than other people, but I think every group of people has bias.
Here is one strange idea:
Information and complexity are requirements for intelligence. Information might even be a primitive of intelligence (and other things). So maybe one obvious observation selection effect is that we observe everything else in our universe as less complex than us. Random vibrations do not make observations, an observation is a complex pattern. So we know of the existence of one "mount improbable", with intelligence currently at the peak. But maybe intelligence does not as generally describe a singular pinnacle of information or complexity as we seem to think. If we think multiple (and strange) universes are plausible, then why not multiple (and strange) mount improbables, all based on information or complexity? So instead of considering ourselves a part of the 'observer' reference class, we can observe ourselves as part of the "complex information" reference class.
I will continue the strange idea with two points.
1) We haven't really explored all of the permutations of the structure of the universe enough to rule out the plausibility of other complex "mount improbables" in alternative versions of our universe. We don't understand our own physics and we haven't even figured out if different values for various seemingly arbitrary constants would always result in low information/complexity.
2) The purpose of the multiverse theory seems to be to "explain away" information. But this is not just Occam's Razor, it is Thor's Axe. Do we have a universal scale of information which our universe surprisingly breaks? Why wouldn't our universe contain information that seems very complex to us? What makes it improbable? Maybe our universe actually contains a "low" quantity of information. If we want to argue for a multiverse, we should find more direct evidence that the information in our universe is/was the result of some information outside of our universe. The probabilistic argument for multiverse is insufficient here because it is simply based on the way we think about our own "particular" universe.
So in other words, if we're going to get strange, why not get really really strange? I hope it makes sense.