While I don't doubt the riskier build orders help, I feel the bigger degree of variance comes from getting lucky with CS's and huts.
I agree strongly with this statement. This is why every SP game I've played since Civ IV's first expansion has been with huts turned off. After my first twenty or so deity wins in civ4, I looked at my HoF, and noted that ALL of the top wins were games in which I popped Bronze Working from a hut, IMO, this is too impactful on the outcome of a game. I'd rather have my "better" wins be due to better decisions and strategy, not because of how lucky I got. Sure, there's always going to be some level of map-luck in a game - in this game, which types of CS's are near you and when you meet them, the quality of the land that you start in for sure, and so on.
But I don't think I'm alone in the fact that I take a certain degree of pride in the games where I performed better, and this, while completely subjective, may be the best indicator of how well you did, at least in your own opinion. And your own opinion is really all that matters because, let's face it, no one else cares about your victories, but you do quite a bit.
But back to the original post, I think there's two reasons why # of turns is a better means of evaluating a victory than score. First, and this admittedly is a weak reason in terms of competitiveness, this game, much like the entire series for the most part, starts out incredibly fun because of how open the options are, then becomes even more fun as you unlock and implement the key game mechanics that move you towards a victory, but then becomes incredibly tedious as you progress those advantages towards a victory condition. The late game is absolutely mind-numbing, so much so that I wish there was something like Empire at War's auto-resolve that was unlocked at a certain advantage in the game. I still maintain that due to the tediousness of the late game, someone could make a good living professionally finishing people's games for them. So the reason why turn-time is a better indicator than score is because you're spending a higher percentage of your turns playing the part of the game that is fun, and a lower percentage of the game in what feels like purgatory. As this is a game and the purpose of a game is to have fun, you're making the game behave as a better game by doing so.
While that may be a weak reason as it doesn't really serve as a litmus test for how well you played (and my interpretation of the "quality of victory" you refer to is based on how well you played), consider this instead. If score is the standard that you're basing the quality of victory, then how would you increase your score? The answer is very simple: delay your victory. Stop building that last spaceship part with one turn left and switch to something else, or don't conquer that last capital but leave it at 0HP and your units surrounding it. Then as the turns progress, your score will increase as your population continues to rise, you build more irrelevant wonders (and districts? I don't know if that impacts score) gain more land through expansion, and so on. The more you delay a victory once it has been more-or-less locked in, the higher your score will be. Aside from the fact that it seems counter-intuitive to equate delaying victory with increasing the quality of that victory, you aren't challenging yourself in any ways by doing so (other than I guess patience.) On the other hand, if you're equating fewer number of turns with quality of victory, then how would you reduce the number of turns needed to achieve victory? The answer here is much harder; but basically it means you need to play better (or not necessarily better in some opinions but rather more efficiently) which is why turn-time is arguably objectively better at determining quality of victory.
