拿…來 puts the object to use as material toward a further purpose; 把 acts on the object itself and changes it. 拿經驗來作例子 uses the experience; 把杯子喝完 disposes of the cup's contents.
拿 first picks up a concrete item, then applies it; 用 names the instrument flatly. 拿筷子吃 lifts the chopsticks into the eating; 用筷子吃 just states they are the tool.
abstract object: 他拿生氣來罵人 → 他拿那件事來罵人 (pick up a concrete thing, not a feeling)
missing downstream use: 老師常常拿自己的經驗 → 老師常常拿自己的經驗來作例子 (the item needs a 來/作 it serves)
wrong frame for disposal: 拿那本書看完了 → 把那本書看完了 (acting on the book itself wants 把)
English 'use X as Y' / 'take X as Y' collapses the two-step pick-up-then-apply into one verb; learners drop 來/作 and leave 拿 stranded.