Most of these abilities only occur when the case enters the battlefield, but they can also be triggered in other ways, such as Case of the Pilfered Proof, which has a triggered ability that adds a +1/+1 counter to your Detectives whenever they enter the battlefield under your control
This makes them a powerful tool for dealing with tough creatures your opponents may control
1 Honden of Cleansing Fire
And thats not all: remove flying counters from your creatures placed on them by Luminous Broodmoth, slow down the aging of Cumulative upkeep cards, like Mystic Remora (or Blizzard, if you feel like putting flying counters on opponents creatures like a monster), allow Undying creatures to continually un-die the (giant robotic manta in the) skys the limit
Peace, love, and have fun Eddie Additional Reading 1
Honestly, I'm not even that great at the strategy