For your artifact problem, I would require the spell Legend Lore to learn anything significant about an artifact. For example, Identify would reveal that an axe is +3, but only Legend Lore would reveal that it's The Axe of Dwarven Lords.
For normal magic items, one way I keep Identify under control is to pay attention to the material components; "a pearl worth at least 100 gp and an owl feather" (5e Player's Handbook page 252). A spell focus only replaces components without a listed gp value. If you can role play acquiring pearls of appropriate quality, the spell becomes a more rare resource. The party will have to carefully pick and choose which items they wish to identify.
A character can use a component pouch or a spellcasting focus (found
in chapter 5) in place of the components specified for a spell. But if
a cost is indicated for a component, a character must have that
specific component before he or she can cast the spell.
-- 5e Player's Handbook page 203
For additional role play fun, I sometimes require the fish component from previous editions. Keeping a fishbowl of goldfish alive while in a dungeon crawl is a significant challenge.
The material components of this spell are a pearl (of at least 100
g.p. value) and an owl feather steeped in wine, with the infusion
drunk and a live miniature carp swallowed whole prior to spell
-- --AD&D Player's Handbook, pg. 67 (emphasis mine)
Identify does not reveal curses on an item. Experimentation is required for identification and attunement via a short rest and the Identify spell requires touching the item. Both the Identify spell and the short rest experimentation could trigger a curse.
5e Dungeon Master's Guide
The identify spell is the fastest way to reveal an item's properties.
Alternatively, a character can focus on one magic item during a short
rest, while being in physical contact with the item. At the end of the
rest, the character learns the item's properties, as well as how to
Attuning to an item requires a creature to spend a short rest focused
on only that item while being in physical contact with it (this can't
be the same short rest used to learn the item's properties). This
focus can take the form of weapon practice (for a weapon), meditation
(for a wondrous item), or some other appropriate activity.
Most methods of identifying items, including the identify spell, fail
to reveal such a curse, although lore might hint at it.
Going old-school again here is Gygax's description:
The item in question must be held or worn as would be normal for any
such object, i.e. a bracelet must be placed on the spell caster's
wrist, a helm on his or her head, boots on the feet, a cloak worn, a
dagger held, and so on. Note that any consequences of this use of the
item fall fully upon the magic-user.
--AD&D Player's Handbook, pg. 67