Going to pull a reverse-Seraiel and point out 1200BC is an earlier DoW date than the one in the most relevant HoF slot with Praets-conquer-the-world strat.
Unreasonably early because you would have to sacrifice a lot for that time. How many cities are we building? There's no justification that taking cities is cheaper than building cities, because both Roman leaders are IMP. What's our tech/eco situation look like? Obviously we self-teched IW, which is a beaker dud. Certainly didn't tech Alpha. Maybe we'll get lucky and do IW + random for alpha, except that you probably don't have any of the small random techs (sailing, masonry, monotheism, etc) either. Probably didn't get writing. Do we even have granaries or barracks anywhere? If the end result is we've got a couple of our own cities, several AI cities, and we're ~10 techs behind the AI, little infrastructure, and every forest chopped, I would call that a disastrous result. There are worse games. It'll probably be winnable, but boy is it an unambitious result for a civ as powerful as Rome. This could be somewhat mitigated by leaving the AI with 1 city and demanding all its techs. But at least one of us needs Alpha to do that, and we need at least writing for it to be profitable. How are we securing that Alphabet is owned here? Are we hoping the AI researched it early? (which we can't know when we click IW and commit to this). The AI is probably unlikely to select Alpha while you're destroying it. Are we self-teching Alpha ourselves, sinking heavy beakers once again into a tech we can't trade? Are we going for a really late Aesth, buoying the high unit cost and support cost with city-raise gold, hoping to get it in time while it still has some trade value left? Are we partially teching Alpha as soon as we get IW hoping to get a straight IW -> Alpha deal in? I'm legitimately asking. I don't know the answer, but I'm skeptical there's a 100% foolproof way here.
Why not wait a little bit? What's the concern here? We're not Persia, the AI doesn't have to be stuck on archer-only phase. It's probably preferable the AI has metal if it has a lot of hill cities. Axes are at best slightly better defenders per hammer cost, and spears and swords are going to be worse than archers. Maybe the AI will find horses and build chariots! I also like to give the AI time to build a wonder like mids so I know which neighbor is the juiciest target. What's wrong with an even later very consistent push? Catapults + Praets will destroy everything in their path until macemen. There's a much bigger window here and a much easier way to conquer back-to-back AIs consistently AND have an economy that isn't backwards. We can utilize IMP. We might utilize IND failgold or forges, or be in a position to get CoL in a reasonable timeframe for ORG courthouses. We can spend some worker turns making cottages. We could utilize some math chops. We can utilize granaries/barracks in every city. There's no risk of a diceroll surprise or a last-second wall ruining the game.
I don't like the argument that things like this are better on lower levels. On the one hand it is totally relevant to AI tech pace and your tech pace (the original topic, sorry :X). But ultimately everything is better on lower levels. Deity is a good stress test. The last time we had this discussion dankok showed off an Emperor game where he sword rushed someone saying it was good. Then Fippy chariot rushed someone saying it was good. Then I warrior rushed two AIs out of the game and said it was good.
I don't think IW is never worth self-teching, but I disagree that "playing Rome" is one of the exceptions for when it makes sense. It still rarely makes sense with Rome, and tends to make sense in the same situations where it makes sense without Rome. Like being choked off at 2 cities, having 4 jungle gems, or being alone on an island with Shaka.