[stouset]

To underscore your point, the original flight plan almost certainly did not transit that region. So the pilot likely wouldn’t have even been aware that there’s a TFR somewhere vaguely adjacent to their intended path.

ATC issues minor deviations all the time and for a plethora of reasons as you mentioned. And those instructions are expected to be followed promptly, not “after I’ve spent a half hour re-reviewing hundreds of possible NOTAMs along the new course”.