Why should our default assumption be that the genealogies are meant to be exhaustive?

this isn't an assumption. the genealogies give lifespans, and at least for the period in which there are kings, those figures actually resemble known techniques used to give dates to things in historical works in other contemporary cultures. part of the function of the P source (which contains gen 1 and all genealogies in the torah) was to give the etiological myths of the J and E sources historical grounding and context, to make them seem like histories instead of fanciful tales.

I'm a Christian, but I think Young Earth Creationists are a bunch of cackling jackasses because they take a stance that's scientifically disprovable and stick to it blindly, grasping onto bad evidence to try to back up a claim that no sane person would ever make, ruining the popular conception of what a christian is.

YECs are cackling jackasses, yes. but they are correct in their assertion that the bible makes factual claims which can be verified (or falsified). of course they are shortsighted in that they cannot look beyond those factual claims. but no more so than the moderate christians who deny that the bible makes claims that could be wrong.