"Allows repeated use of powerful Trainer cards"
So what? It's not like LatiBats is a viable deck in this format even without Hammers, Lasers, Banks, etc. I just get donked even by a Hammerhead with a Strong Energy, Muscle Band and Fighting Stadium. When I play LatiBats, I will need to reuse resources since it takes a lot just to KO an EX (maybe several Ultra Balls which require discards, Energy, etc). I think you know what I'm saying. Reusing "powerful" Trainers doesn't make the game broken. EDITED: Again, the only deck that's broken with recycled Trainers is Seismitoad EX.
I don't think you understand this bullet point completely. One deck's viability is absolutely no reason to determine whether or not to ban a card. I could argue that Quad Bidoof isn't a viable deck in this format, and that it will need to re-use resources to KO an EX pokemon.
The point of this bullet point is that it creates a literally TOXIC environment where decks like Seismitoad-EX can beat even piss-poor matchups like Virizion/Genesect because they have the capability to literally play
more than 4 Crushing Hammer in a turn and not let you play any energy. My friend barely top 8'd at the past Regional Championships in Madison because he was having so much trouble with Seismitoad despite playing a direct counter to it. Re-using trainer cards does, in fact, break the format. If it didn't, Dowsing Machine wouldn't have been an Ace Sec.
It also creates a less skillful format, where decks like Mega Rayquaza can blow through their entire deck on turn 1 with no reprecussions. Without Trump Card, Mega ray can easily still function, but it has to manage its resources much more cautiously.
"Extends the time of battles"
Says the people who reprinted Vileplume with Item lock.
Item lock might make for longer, drawn-out games, but it doesn't even come close to Trump Card. If it did, they would have banned Seismitoad-EX, Dialga G, old Vileplume, and any other item lock card that has ever existed. I watched players who used Trump Card in tandem with Seismitoad legitimately take 10+ minute turns multiple times in the same game. In a format where people are already complaining that 50 minutes isn't enough time for 3 games, I can easily see why Trump Card causes a reason for concern.