Here's a rather out-there hypothesis.

I'm sure many LessWrong members have had the experience of arguing some point piecemeal, where they've managed to get weak agreement on every piece of the argument, but as soon as they step back and point from start to end their conversation partner ends up less than convinced. In this sense, in humans even implication isn't transitive. Mathematics is an example with some fun tales I'm struggling to find sources for, where pre-mathematical societies might have people unwilling to trade two of A for two of B, but happy to trade A for B twice, or other such oddities.

It's plausible to me that the need for consistent models of the world only comes about as intelligence grows and allows people to arbitrage value between these different parts of their thoughts. Early humans and their lineage before that weren't all that smart, so it makes sense that evolution didn't force their beliefs to be consistent all that much—as long as it was locally valid, it worked. As intelligence evolved, occasionally certain issues might crop up, but rather than fixing the issue in a fundamental way, which would be hard, minor kludges were put in place.

For example, I don't like being exploited. If someone leads me around a pump, I'm going to value the end state less than its ‘intrinsic’ value. You can see this behaviour a lot in discussions of trolley problem scenarios: people take objection to having these thoughts traded off against each other to the degree it often overshadows the underlying dilema. Similarly, I find gambling around opinions intrinsically uncomfortable, and notice that fairly frequently people take objection to me asking them to more precisely quantify their claims, even in cases where I'm not staking an opposing claim. Finally, since some people are better at sounding convincing than I am, it's completely reasonable to reject some things more broadly because of the possibility the argument is an exploit—this is epistemic learned helplessness, sans ‘learned’.

There are other explanations for all the above, so this is hardly bulletproof, but I think there is merit to considering evolved defenses to exploitation that don't involve being exploit-free, as well as whether there is any benefit to something of this form. Behaviours that avoid and back away from these exploits seem fairly obvious places to look into. One could imagine (sketchily, non-endorsingly) an FAI built on these principles, so that even without a bulletproof utility function, the AI would still avoid self-exploit.

Can you define "rational/consistent"? The terms are a bit overloaded, especially in this community, and making your definition precise is itself most of the answer to your question.

For example, you give some good examples of nontransitive decider-actors, and if some of them are "rational", then nontransitive preferences can be rational, as you point out. Alternatively, one definition of "consistent" is that a decider-actor will always reach the same decision when it has the same information, regardless of what other options it has previously rejected, which requires transitive preferences.