How many times has she died already? When she was alive, she was either being knocked out, in the background or rescuing civilians. She seemed so pointless and yet had so much potential.

She's died just as much as any other Marvel character.  Characters are only as good as how the writers write/use them.  Jubilee's a vampire now wtf?  House of M made everyone hate Scarlet Witch.  I didn't like Jean till Morrison wrote her (Lobdell did a good job too).   You said she has alot of potential so why aren't writers willing to write that?  Imagine if White phoenix of the Crown joined a battle like the current Chaos Wars. 

Oh jeez. The old "How many times has she died already?" question. She really hasn't died all that many times as people think. The thing with Jean Grey is that most people can only think of the Phoenix Saga and just assume that she keeps dying and being resurrected constantly. 

She's died four or five times, IIRC

It's a good few times.

http://www.comicvine.com/jean-grey/29-3552/how-many-times-has-she-died-now/92-389785/

I never understood her either. She would turn her head and mumble into the wind, or speak with food in her mouth, and randomly faint in the middle of conversations.  
 
lol, Mom jeans.