Using Copycat with one-shot abilities
The whole point of Copycat is to allow you to use another minion's ability. Making it impossible to copy most minion's ability makes makes no sense to me, and it makes no sense to the others with whom I've played either.

Keep in mind that you're already limited to abilities of other player's minions in play (something you have no control over), and that ongoing abilities and talents only work for your turn. This offsets the ability to have some flexibility in the effect of the minions ability.

We have it come into play with the abilities of the minion it copies. Playing a Copycat masquerading as an Enchantress ("Draw a card.") would have you draw a card, because it is an Enchantress as far as any can tell (except in name and power).

It's not really an "again" type of situation. You get to use the Enchantress's ability once. Just like the Enchantress did.