The cards also don't say 'during end of round' (like 'while attacking' or 'during your activation') but *at* the end of round, which is a specific time (like 'at start of round'). I really think it is one window per player, based on initiative order.
I think like some mentioned, it has to do with other future cards.
Perhaps a future card or character can unexhaust an attachment (which makes sense with some of the attachments already out there)