Had to vote the last option, because holy false dichotomies Batman!
"Perfect" balance is, and always has been, an impossibility outside of genuinely trivial gaming. Even chess, itself often held up as the yucky "balance is a four letter word" extreme, isn't perfectly balanced. The person who moves first has a slight but statistically meaningful advantage, which is why chess tournaments always have both players play both sides at least once, often more. The only time you ever hear people actually talking about "perfect" balance is either Thanos memes, or strawmen.
Effective balance does not require linearity, and in fact an actually well-balanced game encourages non-linearity. Unbalanced systems are rife with degenerate solutions (in D&D: be a spellcaster.) See, if the game is actually well-balanced, then the difference between choice A and choice B (and C, D, E, etc., etc., etc.) cannot be boiled down to a mere calculation--because the calculation will tell you that the measurable benefit is basically the same. This means that choices become driven by value-judgment, not by robotic, unfeeling calculation. And, paradoxically, this gain of local-scale predictability (near-certainty on how your abilities work, generally reliable predictions for how challenging a particular encounter will be) thus creates long-term unpredictability, because the things which drive players toward one choice or another will be what they care about and value, not what is optimal or powerful, and a player's motives can change on a dime.
Conversely, for an "unpredictable and swingy" system, players have every incentive to either turtle up, or ruthlessly exploit every fault and error coded into it. If the dice are swingy, don't let them touch you. If things are unpredictable, don't let them become uncertain. Always push play toward the most optimal approach. This leads, almost inevitably, to DM/player arms races and exploitative behavior. The rules are an obstacle to play, rather than a facilitator of play, so they should be avoided at all costs and subverted whenever they can't. Despite gaining moment-to-moment unpredictability, the hand at the metaphorical tiller will have a very clear destination to sail toward, whatever optimal and/or degenerate strategies exist.
I value balance, in part, specifically because it liberates players from the never-ending cycle of seeking to exploit the flaws of the rules, or feeling like you've shortchanged yourself or your fellow players because you didn't. Instead...you can just make your choices based on what you find most compelling: interesting, dramatic, unexpected, befitting the character's personality/history, whatever.
Give me the well-balanced (not perfect!) game that, by NOT being swingy, becomes significantly more unpredictable at the scale of sessions and arcs and campaigns.
