I may be mistaken but English archery seems to go above and beyond what would be needed for hunting. If that was standard hunting practice, wouldn't other continental Europeans have longbows too?
In an answer by /u/hergrim to this question
he/she talks about how the difference in man power and resources lead to different compositions in France and England's armies (I know the OP question is about European countries overall but France makes a good example). France with its large pool of armoured mounted knights lead to armies at were built around big charges in open battle and footmen were for sieges. England however had smaller population and number of mounted armoured knights. So it lead to legislation to train more bowmen from more common folk to supplement their armies.
It's not a full answer on why the the rest of Europe didn't use the longbow but something interesting and related to read while someone comes along to answer.