Let them keep exotics, just no critical strikes when wielding them.
It even goes with the RP of the class. Being so dedicated to the balance, strength and finesse required to be supreme 'blade masters' they have forgone the styles of other weapons such that certain feats may only be accomplished when wielding true bladed weapons.
Basically, I've played this game a long time, maybe not early 1.0 like a lot of you, but it was fairly early 2.0. But even before that, I played AR for about 5 years so I've seen a lot of mud evolution. I've played a wide range of classes to varying levels of success on both muds combined, but mostly I play because of the experimentation value and a bit of 'thrill-riding' if you will. I know that I can be calculatingly deadly in PK and I also know that I can be foolishly stubborn - but somewhere in between I try to find balance in (and out of) the game. I'm not looking to be known as the best PK'er, I know I can hold my own with most classes, some better than others. My only ooc contacts are three other long-time AR/FL players who also like to discuss the game mechanics. So, generally speaking, I don't just pull these things out of my arse.
Now, as for BLMs and exotics - let them keep them, I think the real problem is them being able to perform critical strikes with them. I think that would be a perfect tone. Because it makes them take use of their doublesheath skill if they want to perform critical strikes (if they're smart) so they can still perform the strikes, them sheath/unsheath their exotic (or whatever - you get the point).