That's why I don't play on speed/difficulty combinations that warp the game balance. Suboptimal strategies suddenly become the best ways to win, and well-balanced, long-term strategies allow the AIs to leverage their artificial advantages.
Instead of one human vs. a bunch of Immortal AIs, think of two humans (one Roman, one Egyptian) vs. a bunch of Noble or Prince AIs. The Egyptian player will get a small head start, but the Roman player will be able to go much longer before being blunted by Crossbows than the Egyptian player will before being stopped by Spears. You figure out the consequences of that.
The human using rome getting rolled before he ever sees iron? You again neglected to mention game speed; it's going to matter DRASTICALLY. On mara prats take it easy while on quick the war chariots are disgustingly better.
There are a few things in favor of war chariots you flat-out neglect that really hurt your ability to compare the units:
1. War chariots cost 50% less hammers than praetorians. If a prat wins at 70% while the WC is more like 30% (with withdrawal of 10%), don't forget that some of that variance is made up in unit cost. It's not like surviving WC don't get promotions also.
2. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. 2 moves. Even at a neutral speed like normal, the value of 2 moves is obscene. 2 move units force fights in more favorable locations and FIGHT FEWER UNITS. Prats struggle to effectively fork cities; war chariots do this easily. Prats will see 1-3 additional units/city than war chariots due to extra whip/hammer time while the prats travel. Your perception of the praetorian attrition advantage is therefore overblown. Significantly.
3. War chariots are a lot earlier. AH ----> hook horse, compared to "food resource(s) -----> bw -----> IW (and you need wheel in there at some point too, which egypt starts having teched). Without a strong commerce resource rome will struggle to field material #'s of prats before 1000 BC or even somewhat after. Egypt can have already killed someone off by then!
"small head start"? Egypt is an entire civ up before you even declare with >half your starts (and that translates to a production advantage even FURTHER cutting whatever attrition advantage the prats are getting). And on trash difficulties like noble, it's simple enough to slaughter 4-5 civs with WC anyway; on standard maps that will be virtually every AI. Where's Rome's advantage in this regard?! The if you DO go up in difficulty, hitting sooner before you run into situations like "hill capitol with 5 axes" (not an uncommon sight on immortal if you declare much after 1000 BC) is a big advantage.
4. On top of all of the above, AH is a priority early tech because of the food resources it unlocks. Even for rome it might be your priority tech with some starts. IW on the other hand...is not a priority tech. It's easy to trade for it from the AI since the AI prioritizes it, and if you don't have iron it gives you no utility for a long time, making the WC a safer unit to pursue also.
On anything short of marathon the prat is an inferior rush unit. It requires a large investment without a guaranteed payoff (no iron = you're SoL on the rush and wind up MANY beakers behind) that does not put the civ materially ahead.
You're still grossly underestimating chariots BTW. Not the war kind, just normal chariots. It's amazingly easy with nearby horse to snuff 80% of civs or so using basic chariots on immortal; the 2 move is just that powerful.