Nothing in the spell description online or in the player handbook which says that Identify does not reveal curses. If it's in the DMG rules only, I still think that the Identify spell description should at least contain a caveat such as "The Identify spell might not reveal a curse on the item at the discretion of the DM". Without a disclaimer such as that, I feel like the rule is unfair and punishes players who try to take reasonable precautions.
As an aside, under your interpretation where Identify does not reveal curses, how is one supposed to know if an item is cursed without attuning to it and becoming cursed?
Identify doesn't tell you that it provides you with food and water for the day when you cast it; ergo, it doesn't do that.
It doesn't tell you that you won't receive a free unicorn when you cast the spell as a ritual; there is no reason to suggest that you would.
Spells do what they say, and not what they don't, and formerly speaking a 'curse' is not a 'property' - these are specific terms with specific meanings. The DM knows this, while the players do not need to. This isn't my interpretation - it's the base design philosophy of 5e.
I'd also add, just to note, that most cursed items specifically call out whether Identify will reveal their curse or not, as a secondary back-up. The important thing, though, is that in both cases it is specifically DM-side knowledge that only comes to players if they suffer an ill-effect from a curse. They may not even know they are cursed until they try to unattune from a cursed item (and discover that they can't), or they suffer its ill-effect. That's by and large the point of curses. Cursed objects fall on everyone more or less evenly, without rewarding or punishing anyone more than anyone else - they don't reveal their presence under most common magic most of the time. Some particular items with low grade or obvious curses do actually show up on identify, but when that is the case the magic item itself specifically calls out that it does. These specific cases do catch the incautious while rewarding the diligent.
An example of a cursed item that IS caught by identify is the Armour of Vulnerability:
https://www.dndbeyond.com/magic-items/armor-of-vulnerabilityAnother is the Loadstone:
https://www.dndbeyond.com/magic-items/loadstoneThese items are the specific exceptions to the general rule of identify, which does not include curses in the information it gives; most other magic items make no mention of Identify revealing them, because it doesn't.
Some parallel examples:
https://www.dndbeyond.com/magic-items/sword-of-vengeancehttps://www.dndbeyond.com/magic-items/spear-of-backbitinghttps://www.dndbeyond.com/magic-items/shield-of-missile-attractionhttps://www.dndbeyond.com/magic-items/hell-hound-cloakSome are a little bit more nuanced, and tell you exactly how they foil Identify, such as the stone of ill-luck:
https://www.dndbeyond.com/magic-items/stone-of-ill-luckNote that it highlights the distinction between DM knowledge and player knowledge, even while the player is actively affected by the curse.
Good cursed items are the kind that seem a little bit too good to be true, but also, once the players discover the curse, still leaves them with strong incentive to use the item or to deal with the down sides of the curse, to reap the item's benefits, making it an interesting decision - how far to push it - both for the cursed individual and the party. Curses that are so debilitating that no-one would ever touch the item are poorly made, as are cursed items that make the item in question functionally useless.
At the end of the day, Identify is the "general" rule, and lists the information it gives. The "specific" cases that trump this are the curses that affect some items, in the individual cases where they do ave some form of interaction with Identification - their specific cases tell you how to handle them, such as if and how they appear when identified. The players have the general knowledge - how their spells work. The Dm has the specific knowledge to adjudicate the individual specific results of that when there are exceptions to that generality, such as a curse would be. The Dm has the information to run the world; the players are experiencing the space and get to enjoy all of the surprise twists and unexpected discoveries, both good and bad. For a video game, this generally means that we should really NOT know that an item is cursed until we suffer its effects or try to rid ourselves of the item, unless there exists some external specific warning or other clue.
