I do think there’s a legitimate balance problem there.
In both of these situations, we are talking about cards that provide both removal and threat, being played multiple times. I don’t think that providing removal and threat at the same time is particularly a problem, but playing the same threats multiple times can be. In particular, if winning a particular game means having answers for six Zilliax over the course of that game, then your decklist becomes saturated with things that answer Zilliax. The more room in the deck is dedicated to answering Zilliax, the less plays there will be in the deck that do other things. This makes your deck closer to being a one trick pony, because you can’t fit other options. The fewer options, the less piloting balance.
I think that there is such a thing as too many “copy” effects, especially when on-board threats are being copied. It erodes piloting balance in control decks by forcing redundancy in answers, and it is effectively an OTK for decks that either cannot or will not control it, except without the dignity of actually ending the game in a timely manner. (Titans are particularly bad in this regard, excluding maybe the Hunter one.)
Threats should be diverse. When threats are diverse, answers tend to become diverse to match.
This half, on the other hand, is pretty much just OTK hate. I’m an OTK enjoyer.
I think that Hearthstone deserves hand control options. In MtG I have a long history of hating having Duress played against me — it is The Fun Ruiner — but I recognize it as a necessary element of game design. Hand control is very unpopular with the Hearthstone playerbase, and I think I can feel why, but I also know that my feelings, like most people’s, can be very irrational. I don’t see how you can responsibly have OTK fun without the anti-fun existing to counter it. And I look forward to occasionally OTKing opponents even through their attempts at hand control — just makes the revenge all the sweeter. I can accept some bad matchups.
That said, Hearthstone is currently in some game design Twilight Zone in regards to OTK. As a player, I’m not going to stop loving OTK because of that, but when I have my game design hat on I just kinda throw my hands in the air and give up. It just feels permanently broken — and as a player, I like broken.