Why would you ignore iron working with Assyria? Statue of Zeus is pretty much a core wonder for them. There's plenty of time in classical to make use of your chariots; you don't have to delay everything just to get your UU as fast as possible.
I flatly didn't want to make a unit that was better than war elephants. War elephants are 25% more expensive.
I was contemplating increasing the bonus to 10% per adjacent enemy. Keep in mind this bonus can simply be viewed as a straight flanking bonus. Flanking pretty much works the same way.
For Assyria, we have the Royal Library as the UNW that's available from Writing. That extra boost of

Science can get you much more ahead than what the Iron Chariot can do once you settle a number of cities. Pulling ahead in tech means you'll have better units overall like Skirmishers and Catapults. Let's not forget that, once you are some ways ahead, the free techs you'll get is far more worthwhile than the Ancient Era techs.
On the topic of Statue of Zeus, you have to more or less beeline for it. I think the greediest you can get is Stonehenge into Statue of Zeus (though you are unlikely to go for Pottery if you are going Statue of Zeus). However, you must look at where Bronze Working is. To get Bronze Working, you need Mining researched. Bronze Working gives you Spearman (a decent unit for Ancient Era rushes but not much else) and reveals Iron. Mining is also needed for Construction and that gives you the other UB (Lamassu Gate). To get access to the Iron Chariot, you need The Wheel and Animal Husbandry.
With all of these so spread out, how do you prioritize your techs? If you go for Statue of Zeus, then you are delaying your Iron Chariot and Royal Library. I feel the Lamassu Gate is pretty meh and helps in a more defensive playstyle that's opposite of Statue of Zeus. Statue of Zeus also gives you a Barracks so that's pretty good. However, you now have to research three more techs to unlock the Iron Chariot. What if you have a luxury that requires Fishing, Calendar or Construction? Do you delay those techs?
Since you didn't go for Royal Library, your

Science is going to be horrible, especially since your production has been mostly the key buildings like Monument and Shrine along with the Statue of Zeus. Yes, you might say that you can then conquer your neighbors to get back the

Science. In the event that you went for Bronze Working followed by Military Theory, you have researched 5 techs at this point with 2 of them at the second column. On higher difficulties, you can be sure that the AI will have more techs than you. In addition to the time you spent getting those 5 techs, you also need turns to get the Iron Chariot. Since you have a Barrack in your capital, you will want to build your units and buy you Worker. Let's assume you went Authority and got God of War for your Pantheon for that extra

Production boost. Your

Production in your capital will be okay, not amazing, until you cleared some Barbarian Camps and demanded some Tributes.
What will your composition look like? 1 Iron Chariot with some Spearmen? 2 Iron Chariots and 1 Siege Tower with some Spearmen? By then, what are the odds of your neighbor having both Archers and Spearmen? It's true that the Iron Chariot will be quite strong but you still have to heal them if you are faced with with Spearmen and such. What if your opponent got Skirmishers? These units can make use of rough terrain for hit and run. I think you get the idea that the AIs will be better prepared to deal with Iron Chariots by the time you are ready. The issue is that there isn't a huge window you can make use of it before the AI will have ways to counter it (like Skirmishers and their own Horsemen) and that's also dependent on the terrain. Classical Era, at least when you enter it, will see Iron Chariots harder to use as I know the AIs love their Skirmishers.
I apologize for the wall of texts but it doesn't make sense to me as Iron Chariots have such a glaring weakness and are far too dependent on the terrain. While Statue of Zeus is nice, it's not integral since Assyria doesn't have issues taking down cities with the help of the Siege Tower. It's the question of how you can rid your enemy's units so you can lay siege that's an issue. If you have an AI with lots of rough terrain nearby (Aztecs, Iroquois, Inca), then I'd wish I have Horsemen at my disposal. If you delay your Iron Chariot, then the AIs will have more tools (and more numbers depending on the difficulty) to deal with them.