The standout magic items from OD&D are the staves. They seem like they’re much more powerful than everything else.
Compare the best magic sword with a Staff of Fireballs:
Magic sword: +3 to hit, +0 to damage (so, 1d6 damage).
Staff of Fireballs: Shoots fireballs that do 8d6 damage (save for half). 8d6 is a lot of damage in a game in which the strongest monsters have 12d6 HP. The Purple Worm is the outlier, with 15 Hit Dice, but it will still die in two hits.
And the Staff of Fireball has 100 CHARGES.
Compare that to the equivalent item, Wand of Fireballs, from 3rd edition: it throws 6d6 fireballs and has 50 charges. Furthermore, in 3rd edition, monsters have d8 Hit Dice, and they have more of them. (For instance, dragons have 5-38 HD instead of 5-12 HD.)
Not only that, the Staff of Power is like a Staff of Fireballs with a bunch of other abilities. The Staff of Wizardry is like a Staff of Power with a bunch of other abilities. Between these 3 items, about 10% of staves have the ability to fire 8-die fireballs. You only have a 2% chance of getting the sword +3.
The Staff of Fireballs family might not even be the most game-changing staves in the game. The staff I’d want is “Staff of Secret Doors and Trap Detection.” It has 100% chance of detecting both; it works within 20 feet; and it doesn’t have charges. It’s operational as long as it’s being held. It’s SO MUCH better than having a thief in your party, guys.
Traps (and secret doors) are such a major part of OD&D-style dungeon crawling that I can hardly imagine them removed. Imagine a campaign where that entire aspect of the game was thrown away. I think the DM would have to resort to semi-cheating in order to downplay the staff’s power: “Well technically the lever that turned you all into insects was a TRICK, not a TRAP.” “You detect a trap in the corridor which is THE ONLY WAY OUT OF THE DUNGEON.” “I know you can detect secret doors, but the treasure was hidden behind a CONCEALED DOOR.”