The combination of Delinquent, Red Card, and Peeking Red Card was banned because it allowed one player to get another at a stifling disadvantage from turn 1, effectively stopping them from producing any kind of strategy and forcing them to either get lucky in order to get back into the game or just be left in the dust. :P
Heres a scenario:
First off, let’s say your opponent starts with a Stadium, a Delinquent, a Red Card, and a Peeking Red Card in their hand. They play the Stadium, then the Red Card, and then the Delinquent.
You now have 1 card In your hand, 3 discarded cards, 6 Prize cards, 1-6 basic Pokémon in play, and a draw deck of 49-44 cards. Even if you have 4 Hau, 4 Lillie, and 4 Professor Kukui, you are still in trouble.
If you had one of those cards in your hand, it doesn’t matter, because they just played Peeking Red Card to shuffle it out of your hand, and if you didn’t have a card to deal with this, PRC doesn’t force a shuffle. The odds of you getting 1 of 12 (or 9 if Delinquent made you discard 3, and 3 if Delinquent made you discard 3 and 6 are Prize cards) drawing cards is too low, and they might not even be enough to come back.
Your best chance at drawing a card that might help you is 27%, but most decks won’t run 4 copies of 3 different draw cards, nor have 6 benched Pokémon on turn 1. Your left with one card in your hand, and have to hope you top-deck energy, evolution cards, and or draw cards to use, but much more likely your Basic benched will be picked off one by one while being unable to act without energy.
Even though this loophole exists requiring 4 cards (which you can bring 4 copies of each, and execute later in the match, when the opponent has lost more drawing cards), it is a very toxic and anti-competitive play-style whose only counter-play is luck, and these are the typical kinds of loopholes that PTCG and other TCGs usually ban. The game should be fun and fair enough. This loophole could give most top decks a difficult time if it ever saw tournament use, and it’s not because it’s “skillful” or “better”; it’s too unfair compared to other cards and game mechanics. There isn’t any answer to this threat other than luck.
Source: Red Card, P Red Card, Delinquent, TCG Experience
Hope I Helped!