The fact that in a battle between two equally skilled players, any small detail (like a hero with +1 crystal per day) can decide the outcome doesn't make mirror matches imbalanced in the normal sense of the word. Because imbalance is a situation where a player who is weaker in skill wins solely due to the random distribution of items. There are very few such situations in L-sized mirror matches.
A mirror tavern is definitely needed, but when it will appear is unknown. Wizart has disappeared somewhere, and the HotA team isn't too eager to create similar functionality from scratch. It's not that it's completely impossible, but it's not a priority at this stage.
However, I predict that even if a mirror tavern appears, there will inevitably be those who will still complain about imbalance. They'll complain that the color of items matters, or that the treasure chest is too random, or that morale/luck are not distributed symmetrically, or something else like that. Complaining about the random distribution is an integral part of the Heroes mindset, and it cannot be solved by simple methods like a mirror match.