I think it would be nice if there was a maximum number of moves in one turn. For you as well as for your opponent.
Let’s say the maximum number of moves in one turn is 3.
The 3rd time you make a 4/5er, you don’t get an extra turn anymore, and it’s the other player’s turn.
You could even have a 3rd trait on some cards that raises the maximum number of moves per turn by 1.
This would remove the cheesing from either side, where one player just gets 10 to 20 moves in one turn.
While I understand the frustration that the AI going on crazy runs can cause… what you are suggesting is a permanent freeze that exists within the game mechanic itself… a PERMAFROST, if you will.
Since Freeze is generally regarded as one of two status effects that should have never been introduced in the first place, Deathmark being the other, I do not see this garnering much support.
Sorry… 
I love me some looping teams. They’re what lets underpowered early- and mid-game players take down the maxed out end-game teams – if your opponent’s 40-Attack Marilith never gets to take a turn because you keep switching between spells on your end, you never have to worry about how your Golem/Treant doesn’t have its Stoneskin trait yet.
If there was a dislike button, I’d hit it. There are many different ways to play the game, and looping teams is one of them…
I can’t support this idea either. I think looping is a legitimate option in the game.
That being said, I would love if they added a skip animations button so that you didn’t have to sit and watch a long AI loop. That would be heaven.
This!!! Sitting and waiting for the AI to make its 10 moves is one of the most annoying things in this game - even (maybe especially) when the enemy has the last troop alive with 5 HP and you have all 4 AoE spells ready to cast… 
On-topic: I don’t like the original suggestion. However I think it may be a good one if real-time PvP is ever implemented. But only for that mode.
Sirrian actually mentioned that they limited looping in real-time PVP in one of their old games. The limitation makes since under those circumstances.
Yes, a turn limiter in real time PvP is TOTALLY acceptable! 
On the topic of skipping animations, what if they just implemented a Speedy AI turn, where the game just runs runs all of the computations for the AI turn and then displays the results and its your turn again.
If that was not clear, it would look like this:
Make a 3-match that fills Valk
Board appears to shuffle before your eyes,
Several troops loose armor and life, one troop is frozen, first troop entangled, last is burning, AI mana totals have changed two enemy troops are ready to cast now
Cast Valk
So no time at all wasted on AI turn, just make a move, observe the AI results, make your next move.
I think this would be a great idea for a new game mode. It would mean you’d really have to think twice about converting gems, because if you left too many on the board you’d hand the turn to the opponent.
Unfortunately I don’t think such a mode would be compatible with death mark - if turns are really short it makes death mark way too powerful.
My favorite decks to play manipulate gems and matches. If my turns were restricted to 3, I would finally start playing other games.
Agree, too dangerous an idea to hit the main game. But not a stupid idea in itself and I like the minigame idea.
I once suggested a game mode with a ‘flux’ bar. Every time you collect mana, the marker on the bar shifts your way. When the enemy collects, it shifts their way. If the marker gets to either end of the bar (i.e. one player collected a lot of mana without the other doing so) then a flux / chaos hits, and:
i think its great idea for a live pvp mode
but in player vs ai modes there is too much punishment to the player side in it so i dont think its worth it, after all ai doesnt get frustrated neither pays the dev bills
I know that there needs to be a counter to ETs, but Freeze slows the game down to an agonizing degree.
Where the sweet spot is where the counter exists without the excruciating slowdown, I know not.
One idea thrown out completely haphazardly with no regard is an affix such as Chill or Sludge or “foes take X damage on extra turns” or something.