mikemcmann wrote: That makes them seem quite fragile.
As stated by others you've got it right, but also consider a few things:

Elephants get an
additional +1 to death rolls, so whilst their biggest fear is being shot at, they have to take at a minimum 4 hits before they even
risk being killed

Elephants
were fragile and fickle\

at 50 points for a BG they seem expensive, but not in reality. Most BG's are bigger and seem to have a lot more resilience, but in reality Elephants when used correctly can be a big headache to your enemy. Put them in the open by themselves surrounded by archers and you'll lose them, but that's the same as charging superior pike with knights... the wrong thing to do. Use them right and they'll be tough.

Just because you have them doesn't mean you have to use them. Sure, 50AP and a pointy stick part of your army is hard to not use, but if it doesn't have a place in the current battle try to use it in an intelligent way. Many mounted troops are used in BG's of 4, so they Elephants can give rear support to them if nothing else, so design your army to take that into account.

Elephants disorder cavalry they are within 1 base width of. Thus, if you have a formation like this:
with

being Cavalry and

being Elephants - this is what happens:
with

being disordered cavalry.

get 2 dice. They lose 1:3 dice due to being disordered. How many dice do they lose? ZERO!
So, if your enemy come across you like this:
with

being Knights and

being blank spaces
Then the knights will be overlapped in the melee phase. Unless they do great execusion to your cavalry in the impact phase (which they may do, but may not either) then you'll have evened up the odds dramatically.
If they come in any other way - they are going to have to fight elephants at an extreme disadvantage.
It's not quite as simple as that, but I don't think Elephants are a waste of AP's, you just have to use them intelligently, and protect them from things they need protecting from

... but that's what Elephant runners (light infantry) are for.
Hope this helps.
Ian