Ah, you're not looking in the right placeIt says it reveals the properties of the item and there is no mention that I found in the spell or in cursed items that gives exception to this in 2024.
It is actually most of the usefulness of the spell for magic items.
Otherwise it is just for learning what spells are active in a creature.

5e24 DMG:
Cursed Items
A magic item’s description specifies whether it bears a curse. Most methods of identifying items, including the Identify spell, fail to reveal such a curse.
Attunement to a cursed item can’t be ended voluntarily unless the curse is broken first, such as with a Remove Curse spell.