I understand your frustration, but to be honest, she's only two! She's still very much a baby & having a binky during nap & bed time will not cause her harm (especially if you use an orthodontic binky such as Born Free, EcoBinky, Nuk...).
Around 18 mos or 2 yrs we started to wean our daughter off of it during the day. Unless she was sick or teething, she pretty much only got it at nap/bedtime.
When she was about 2 1/2, since SHE was ready, we talked about it a lot & then made a deal w/ Santa that she'd leave her binky's for him, so that he could give them to all the babies who didn't have any, and in exchange, he'd leave her a very special, big girl gift. He left her a tricycle under the tree that year. And it worked out well b/c she was ready.
As long as her speech isn't impaired (which almost never happens unless it's in her mouth 24/7 AND she's over 3 yrs old), I really don't think it's anything to be overly concerned with, myself.
Again, I really do understand your frustration, but this seems to be something that she really needs at this point still. If it were me, I would try to wean her off of it unless she's in bed and start giving her something else to occupy herself with or give her extra, extra attention, etc...
Don't worry--she'll give it up when she's ready to!
Good luck!