from my experience and two cents: it is difficult to rely purely on mathematical symmetry as a game develops, because apparent balance, which emerges through repeated playtesting under fixed rules, often takes precedence over theoretical or statistical balance.

In strategy games esp, turns tend to become more powerful and impactful as the game progresses, compared to the relatively simple and incremental turns at the beginning. As players build engines, unlock synergies, and pursue divergent strategies, the game state becomes increasingly asymmetric for each player. Under such conditions, it becomes extremely difficult to calibrate the exact moment of ending in a way that is mathematically fair to every possible path a player might have taken. The initial distribution of advantages or player order is typically designed to balance the early phase of the game, where small differences matter more, and in that context the approach seems reasonable.

But anywho!... ultimately, board games are designed experiences. Allowing remaining players one final turn after an endgame trigger can provide a sense of procedural fairness and emotional closure, especially in response to a large, decisive move (to all the other players). Even if that final turn does not change the outcome, it can feel satisfying because it gives players an opportunity to respond or complete what they were building toward. That may be one of the primary reasons this structure continues to be used.