If the cost of a card goes into the other player's memory it becomes their turn after all effects have played out, so it's a huge game of risk and reward or simply trying to give the other player as little memory as possible so they're not able to play much on their turn
Promo Info EXTRA BOOSTER DAWN OF LIBERATOR [EX-11] CLOSECLOSE EX11-059 U Tamer Parallel Rare Reina Oumi Color Yellow Purple Form - Attribute - Type NSo/LIBERATOR DP - Cost 4 Digivolve Cost 1 - Digivolve Cost 2 - Upper Text [Start of Your Main Phase] [On Play] By trashing 1 [NSo] trait card from your hand, Draw 1 and gain 1 memory
Beckett Shield Thick Card Size Sleeve boxes contain 15 packs
Elixir Rarity: Uncommon TYPE: Artifact SUBTYPE: - CMC: 1 Mana cost: USD: $0.24 EUR: 0.08 TIX: 0.03 EDHREC RANK: 8642 This artifact enters tapped
In addition to being able to search for a card during the end phase, this card is also great for ritual and fusion-based decks
I doubt that this is going to be commonplace, but I did want to say that I think the Rules Committee will take action if this actually becomes a recurring problem