Since resting identifies magic items, and the identify spell doesn’t spot curses, what is the role of the identify spell?

The most important factors are time and convenience. During a short rest, which takes at least 1 hour, a character who meets the qualifications can determine the properties of one magic item (see “Identifying a Magic Item” on page 136 of the Dungeon Master’s Guide). In contrast, casting the identify spell takes only 1 minute (or 11 minutes if it is cast as a ritual) and can be done when a quick determination is needed.