A strategy game (and the only strategy game) I remember being really enjoyable was Fire Emblem Awakening, and yes I would attribute its fun to not just balance, but incredible fruitiness and great art. (For context, Fire Emblem is a series where you move little high-fantasy units around on a grid battleground.)
There is a lot of intransitive balancing in this game : swords are strong against axes are strong against lances. There was elemental magic, and archers being affective against fliers, etc. It all felt very intuitive and allowed each of the many unique units in your army to have a use in battle. Not only do the intrinsic properties of each unit have strengths and weaknesses, but the player could customize units via declassing or weapons, all of which were pretty fruit in my opinion. It created a very diverse and intuitive experience.
I will also mention an instance of transitive balancing I found memorable: you can recruit a weak peasant Donnel as a unit, and discover that he gains experience and strength at very high rates, as opposed to a knight you start with Fredrick, who is very strong but grows at a very slow rate, eating exp and possibly falling out of use.
I will now talk about everyone’s favorite class, the Dark Flier, a female-only flying unit which could acquire the skill Gale Force: this allowed them to make an additional movement on the condition they defeat an enemy on their first movement. Combined with a massive movement range and terrain tolerance, use of a Dark Flier, or at least a unit with Gale Force, is a strategy players lean heavily on. However, I would not call this unit unbalanced, because it doesn’t make the game feel too easy or boring for many reasons. The added sounds, visual effects, and slow motion animations of a skill being activated always makes it satisfying, and only a limited number of units can take on this class. The premise of a dark magic wielding, woman only pegasus rider added both variety to the gameplay and fantasy to the whole experience.