But I suspect compartmentalization might actually be the natural state, the one that requires effort to overcome.

Look at it this way: what evolutionary pressure exists for NOT compartmentalizing?

From evolution's standpoint, if two of your beliefs really need to operate at the same time, then the stimuli will be present in your environment at close enough to the same time as to get them both activated, and that's good enough to work for passive consistency checking. For active consistency checking, we have simple input filters for rejecting stuff that conflicts with important signaling beliefs and whatnot.

OTOH, there's no evolutionary pressure for something that sifts through your entire brain contents, generating arbitrary scenarios where two pieces of information might conflict or produce some startlingly new and useful idea.