Personally I think cursed items fall into 3 categories:
1. Magical mishaps. In these instances, the item was intended to be a specific magic item, but the creator failed in some way. The resulting item has some beneficial properties (maybe less than the real item, maybe even more), but a drawback. Ideally the drawback and the benefits are balanced such that the players will consider keeping and using the item regardless, and simply mitigating the problems. Demon armor and the axe of the berserker fit this mould, however typically I would not add the "no, you can't drop it" clause to either item. Items in this category reveal all of their properties with no mishap when identified, but experimentation will sometimes only reveal the positive benefits (in general I don't allow "short rests fully identify items" because it's more fun to do otherwise).
2. Items designed for a specific but unusual purpose. The girdle of masculinity/femininity falls in this category. This covers items that were designed for a specific purpose and a specific owner that have unusual effects that may or may not be desirable. In the case of the girdle, it's obvious what the owner wanted. I would reflavor it such that instead of simply being non-removable, it melds into you and disappears. You can't remove it because it is no longer physically there. That's an item that I could imagine some specific individual might pay good money for: it's 'curse' is a desired feature. bags of devouring or dust of choking and sneezing (depending on who made it - anything that doesn't breathe loves this) might fit this category. Identify will reveal these for what they are, but not their intended use.
3. Items designed to be traps. These are kind of a sub-category of 2. The girdle might have been deliberately given to someone important in order to disrupt a succession or similar. A bag of devouring might actually be a physical manifestation of an interdimensional creature designed to eat items. A scarab of death is handed over in an assassination attempt. The aim is hostile. Such items are deliberately warded so as not to be detectable with magic, or to be detected as some other innocuous item. As such, identify gives false information or triggers the item.