My first question is whether the goal is to mill your grain/malt as fine as possible while avoiding stuck sparges?
Yes. Ideally you probably want zero intact kernels, just a bit of flour, and plenty of intact husks, cracked apart enough to expose the white goodness inside.
Second, I gather that stuck sparges are more of an issue with fly sparging, so can batch spargers afford to mill a little finer than continuous spargers?
You can still get a stuck sparge when batch sparging, so you probably don't want a more flour in your grist.
Finally, are there any other substantial problems with milling too fine other than stuck sparges?
No. BMC actually mill their grain quite fine and use a more sophisticated system than homebrewers (one I don't fully understand).