Documentation on this is limited, so here's a paste! Discovered by magpie of the Battle Facilities community.

On any turn of a Generation 3 game, there is a 20% chance that all Pokemon holding a Quick Claw have their Speed stat maximized. When multiple Pokemon are holding Quick Claw, the game does not do separate checks for each one. This means you can partially "counter" an opposing Quick Claw user by holding your own Quick Claw.

Example:
- Your Metagross has 117 Speed. Opponent's Rhydon has 60 Speed.
- If only Rhydon is holding a Quick Claw, Metagross is 80% to go first, and Rhydon 20%.
- If both Pokemon are holding a Quick Claw, Metagross is 80% to go first, and it's a speedtie 20% of the time (so 10% Metagross/10% Rhydon). Thus Metagross is 90% to go first and Rhydon 10%. Giving Metagross a Quick Claw halves your chance of getting hax'd by Rhydon.

Most Quick Claw holders at the Battle Frontier are quite slow, so you can run your own slightly faster (but still slow) Pokemon to both counter the Quick Claw users and occasionally strike first against faster Pokemon. A good example is offensive Snorlax, whose stats and moves don't synchronize particularly well with other good held items.

This mechanic is most useful for speedruns because they want to avoid time loss from Leftovers. That leaves an open spot in the "holy trinity" of Gen 3 held items (Leftovers, Lum Berry, Choice Band). If your team has a suitable Pokemon, Quick Claw is probably the best bet!