Hmm... last second priority.... let's have a look-see.
Sturdy users will appreciate this. Forretress can get one last Rapid Spin or Stealth Rock when hit by a Fire attack. Crustle can Shell Smash, live a hit, and then get one last priority Stone Edge. Heck, we could even start seeing one-of-a-kind movestets. Imagine this: Skarmory is slammed by Mega Charizard's Fire Blast. But she hangs on with Sturdy! Then, blam, priority Tailwind! Suddenly you've gone from losing a match to surprising your opponent with Skarmory's Tailwind and your net Pokémon's doubled Speed! I'm not saying that is what will happen, it's just what could happen. (In other words, something that only my odd brain could think up.)
Bulky Support Pokémon
Are you tired of your Cresselia being too slow to use Lunar Dance before getting KOed? Well, Custap Berry is the Berry for you. If your support Pokémon is on its last legs, never fear. Custap Berry is here! Just imagine: Priority Wish, priority Screens, priority Heal Bell, priority Recover… the list goes on.
Gimmicks, I predict, will be the most common user of Custap Berry. The Tailwind Skarmory that I suggested above is one of them. Others include priority Destiny Bond, priority Will-o-Wisp, and priority Memento. Like I said, these are all just gimmicks, but useful gimmicks nonetheless.