It's not inflexibility in victory conditions that makes Babylon dull, it's inflexibility in the playstyle you're forced to use regardless of which VC you go for. Science and diplo require the same tech path; Domination requires the same tech path long enough to seal your science advantage and maximise GS spawns before taking aggressive techs. And then warfare just becomes dull because you outtech everyone else so far that it's just a matter of wading through inferior units. After all, what makes the game enjoyable is the way it plays on the way to victory, not your specific victory condition. A civ that can take any of two (marginally three) victory conditions but has only one way to get there is much less engaging than a civ that might, say, be optimised for fewer victory types but has more leeway to vary its strategy for achieving that victory. The example given even demonstrates that a strategy that forgoes going for early Education doesn't work past King.
No, it's neither broken nor cheating. Just lazy, uninteresting and ultimately suboptimal, as well as being far more situational in its application than top-tier civs. No civ that requires the qualifier "in single player", or that doesn't work well on smaller maps, deserves top tier status Arabia in some regards is like Babylon in vanilla, which revolved around using the GSes spawned to slingshot for specific techs at specific game stages - favoured because it could exploit one particular strategy very well. Arabia is not a strong economic civ; 240 gold per lux every 30 turns in the early-mid game is not going to match the gold-farming of some other civs long-since departed. As I noted earlier, the strength lies in having specific amounts of gold when you need it for highly specific purchases - as with vanilla Babylon relying on having a GS when it needs it to beeline for a very specific tech (and look how many people were crying that Babylon had been "nerfed" as soon as this became impossible). Arabia is a civ that seems powerful because it can perform a specific strategy well; unlike Babylon, however, it is a civ that is not particularly powerful more generally.
As for what the developers intended, what they likely intended was for the Bazaar to allow Arabia to maximise happiness by trading luxes for other luxes, which fits the theme of a bazaar well. As I've noted before, the AI is badly-programmed to use its gold, and the developers do seem to have made efforts to improve it in this regard which suggests that Askia sitting on 10,000 gold at a time is not intentional. Certainly it would be bizarre if the developers really had intended that the gold bonuses given to the AI at higher levels should be used to make the game progressively easier for the human player, which is the result of lux-for-gold trades against an AI which gets bigger and bigger gold bonuses but never spends any more. Yes, they undoubtedly intended lux-for-gold trades to be viable, or they wouldn't have coded the option, but it seems unlikely they intended that the AI would have spare gold to trade so often that a player could reliably farm it for half the game. Even if they did, as above, this is bad programming.
Not correct - see above. You are not going to be using Arabia to spam-buy units or maintain a large army with its gpt, for instance, to rushbuy courthouses or research labs en masse, to shore up alliance with half the city-states on the map, or whatever, at least not on the strength of its UA without augmentation from Tithe, Macchu Picchu and other effects that let any civ do the same thing. Persia can do that; Songhai can do that. In contrast Arabia gets moderate amounts of gold as quick lump sums that it needs to spend carefully to be effective.
Much less of an issue post-G&K, and it's very much an either-or with Arabia. You have limited luxuries the other civs don't have, and limited civs with which to trade, as well as the gold boost you get for it already being fairly moderate, without lux-for-lux trading.
This is a very bad way of looking at it. The Keshik belongs to a warmonger civ; the camel archer does not. UUs only make sense in context, not in isolation. The Camel Archer as an Arabian UU is much less useful than the Keshik as a Mongol UU or the Cho-Ko-Nu as a Chinese UU. All the moreso because, to maximise its trade returns, Arabia needs to remain peaceful with the civs that don't have the luxuries it can offer. In isolation the Camel Archer is a great UU, but in the context of Arabia as a civ, it doesn't do a lot to push them up the ranking.
At exactly the time you can't afford one because your lux-for-gold trades have either run out or are generating too little gold to stimulate your economy...
Well, of those I only do the former as Songhai (there's a cap on the experience you can get from barbs) and the second only if they don't want much (which usually requires set-up of some form in order to make them dislike the AI you want them to declare war against). But you'll note three clear differences:
1. "making use of all of the options and strategies available" is a far cry from making use of a grand total of one of them.
2. Every one of these requires some degree of effort, and trade-off - units farming barbarians or bullying CSes aren't somewhere they may be more useful, and are costing you maintenance into the bargain; AI bribery requires an AI willing to go to war with another as above; outmanoeuvring the AI again still requires an army. None is a case of being given a free resource you can just give away for no penalty.
3. None of these (except outmanoeuvring the AI) is the basis of a viable game-long strategy. Arabia revolves around using a single technique that requires little effort and exploits badly-programmed AI gold-hoarding as the entire basis for its high place in the list. If you want to compare this with farming gold from barbs as the basis of a strategy, fine - in that case Arabia deserves to rank as high as the Songhai. Except of course that even Songhai doesn't rely on farming barb camps indefinitely, although it can use them to get a strong headstart.