InvisibleStalke
Emperor
I don't see what special threat engineering affords. There will be some pikes but typically the unit you have to get through remains the longbows (they're a lot more prevalent, and elephants will tend to have shock, not cover. Lbows will have CG, pikes will not, so pikes will only be marginally better than them and more rare). If pikes are really a problem just CR axes or even swords will usually handle that. The most painful enemy tech jump points for cat/axe/elephant are feudalism (where every city defender will cut down way more catapults) and gunpowder.
Engineering brings two threats - castles and pikes. Castles mean that suddenly catapults take forever to knock down defenses - and launching attacks against longbows and pikes behinds +100% defenses doesn't get you very far.
Pikes on defense do very well against elephants - and your CR axes and swords won't be attacking them, they will be fighting longbows or crossbows instead. Which means that casualties will mount quickly as every attacker is well countered.
I agree feudalism is going to be painful - but as long as you can knock the defenses down reasonably quickly and pummel the longbows with a few suicide cats, elephants can take down longbows. Unless of course we are talking about a protective leader - CG3 longbows will laugh at this attack.
Muskets can, of course, kill anything in that stack with relative ease. Generally speaking though this stack is good until then with some exceptions. HRE really can screw you with engineering since the axes won't hold. Japan can make things miserable as elephants are not immune to first strikes and shock elephants aren't going to have flanking II (and toku will likely have access to formation if needed on his UU). China will screw you just with the collateral. Rome will get in the way with its UU even though you can still beat it. Finally, while SB doesn't get any units that would especially dominate this, massed CG III archers from a high unitprob AI is just loads of "not fun" for a catapult war.
Muskets aren't too much of a threat - you never face too many of them as the AI can't insta-upgrade to them. But I've never seen the AI with gunpowder and not engineering, so I am probably consolidating by then.
Any protective leader will definitely screw you with engineering and half price castles. In fact they will probably screw you at feudalism/machinery. I don't particularly fear AI CNK's - they don't really know how to use them. And Toku will take forever to get Samurai's so they aren't a concern.
Of course, all that is for the AI. Any effort involving massed siege defensively will seriously reduce the life span of this stack. Combat longbows or even axes start getting >50% odds vs elephants somewhat quickly after a few cats. AGG and PRO hold an advantage in this realm of course, as both have access to formation after 2 promotions. One doesn't see many formation longbows from a protective AI, but if you think about it that would actually be threatening to elephants as elephants can't get cover and aren't typically immune to those first strikes. ANY collateral would set the elephant pretty far back vs a feudalism PRO guy. Of course, C2 formation would be serviceable against shock elephants post-siege, too.
Luckily the massed seige will be on my side vs the AI

Its not worth putting formation on a protective longbow. The problem is that most units formation is good for are immune to first strikes and drill 2 is wasted. On defense CG3 would be much better and on attack you don't get to pick your defender so more general purpose promotions are more useful.
So while elephants are very, very good, the extra very is from AI stupidity. Otherwise they're just very good.
The same is probably true for Praets, Immortals, Quechas etc too. Eg a human player can just build warriors to neutralize Quechas. I think war elephants are in the same league as the more powerful UUs - but are essentially a random UU that you can get if you have the resource, regardless of the leader.
I like them for that - but I would like ivory to be rarer - the most likely counter to your war elephant stack is another war elephant stack since one deposit of ivory often means there are more. And I'd like to see a few other rare-resource-units to add a bit of flavor.