I think playing a mind flayer would ruin flayers as an enemy. Some sorts of enemies, like Klingons, become more interesting as you better understand them. Other sorts of enemies, like the Borg, become less interesting as they become understandable.
Klingons have complicated politics that center around houses and codes of honor. More you find out the more interesting they become. So it is with the drow -- houses, favor of Lloth, etc makes you want to learn all you can.
Other enemies, like the Borg, become less interesting as we learn more about them. The Borg were frighting because they were they were immune to reason. We are after you, our technology is superior to yours, prepare to be assimilated. Likewise with the alien in Alien (the movie). There is no reasoning with the alien to it you are a) a two legged nursery and b) food. Do you have conversations with your food?
Once the Borg started talking, once we understood them, they became like every other enemy.
The flayers are terrifying because they are a collective mass without identity. Adventurers are beneath their contempt -- the food should be quiet. The Illithid are not individuals, they are a collective and their mind is like that of an insect colony. Join the colony and you lose yourself -- you die and your experiences are overridden by your new identity. If the metamorphosis is just a skin for another playable race the flayers become less frightening and less interesting.
Or, to throw out another analogy, flayers use the zombie template and not the vampire template.