I strongly suspect for the points you're making you tend to play on very easy game settings, so you're used to just conquering anyone in sight. When this isn't true, you'll see why God-King is much more useful, because you're not guaranteed tons of cities and no threats or aggression against you. Also remember that it's usually VERY easy to find a great capital to start with, you can explore around with the settler and its bonuses, on most maps you don't have to settle in place immediately.
So, to discuss the Khazad, I'd think that a huge portion of your early game is incredibly subpar. When do you found your cities, and how do you keep up the vault without any civics at all to help out? If you don't found your second/third cities in REX style, which you really shouldn't due to the vault, I wonder if you just sit there with your capital in despotism out of stubbornness, because researching Mysticism can't possibly have any benefit

With God-King you can get your vault up very fast, get an incredible RoK city, and build anything you want.
Not only that but Aristocracy works great with mines because of the generally more abundant food throughout your empire.
You seem to fundamentally misunderstand the malus to food with Aristocracy- it does NOT work great with mines, since in fact it causes a lesser amount of food in your empire compared to what you'd have without Aristocracy. So less food = fewer mines = less production, which kinda hurts the Khazad given how they have nice bonuses to production and all. Until you get Sanitation you really won't be able to feed mines all that well, and beelining Code of Laws + Sanitation together is risky enough with any civ and simply dumb with the Khazad - it ties into none of their strengths.
The one thing you are right about is that a game with Kandros Fir would do well with Aristocracy, but only because he is an excellent leader for an excellent civ in the first place. So the same game would likely do much better with early GK, and then choosing from whatever civic best suits his needs as the game goes on. But please, if you must set up an Emperor+, standard settings comparison with the Khazad, and we'll see how it goes too. I said before that I thought a Khazad comparison game would be overly unfair on Aristocracy but if you don't think so I would be glad to participate.
And yes, I have used Aristocracy to great effect in various games, which is why I realize it is useful in some situations. But this mindset of beelining the civic from the start still seems incredibly backwards, it misses out on so much else that works better.
Also, 150 save is up, I did it just since you've been going on about that game. It clearly does quite excellently in many stats, and that's on my first time through again, could have been a lot better optimizing the starts. If you want to play from there, "non-retardedly", if you can, you can also see whether it would be better to go to Aristo rather than City-States; I'm just guessing City-States is fine so not going to waste my time, I already did what you've asked enough on the game. A quick religious victory with 80% population seems very possible so just see whether Aristo or City States works better with that expansion - I think the maintenance benefits of City States are quite clear on their own.