Thus, to be coherent, we need to ensure that our beliefs "fit together" (logically).
Yes, but for a cognitive system to make its beliefs about a large number of complex and interdependent statements "fit together" (logically) requires infeasibly much computing power.
The brain doesn't do it and nor will modest-resources AGI systems.
To avoid a dutch book, an entity need only check first before acting to make sure its relevant assumptions are logically compatible.
Yes, but this in case you didn't notice, checking whether a set of Boolean expressions are logically compatible is NP-hard, and checking whether a set of quantified expressions are logically compatible is uncomputable... ;-)
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