Until 5 minutes ago, I thought the purpose of using Identify would be to detect curses or similar effects that aren't revealed by spending a short rest experimenting with the item.
However, that's when I stumbled over the following paragraph in the DMG (p. 138/139, emphasis mine):
Some magic items bear curses that bedevil their users, sometimes long after a user has stopped using an item. A magic item's description specifies whether the item is cursed.
Most methods of identifying items, including the identify spell, fail to reveal such a curse, although lore might hint at it.
A curse should be a surprise to the item's user when the curse's effects are revealed.
Attunement to a cursed item can't be ended voluntarily unless the curse is broken first, such as with the remove curse spell.
So, turns out Identify won't actually detect curses on magic items (which is also not directly hinted by the description of the spell. Not sure how I came to that misunderstanding).
What's the purpose of even bothering with Identify, then? Unless your DM disallows identifying items during a short rest ("Variant: More Difficult Identification", DMG p. 136), I can't imagine many situations where figuring out an item's properties would be so urgent that you can't wait for a short rest - or at least not if curses aren't even revealed.