I remember Denise Crosby saying (about her funeral speech), "If I'd gotten more scripts like that I would have stayed."
My problem with Tasha Yar was that I could not believe for one femto-second that someone with that many hang-ups, that raw and that insecure would have been tapped to be a department head / Tactical Officer / Security Chief on a major ship like Enterprise. Interestingly, when I saw her in "Yesterday's Enterprise", she was every bit the seasoned, competent, cool professional that I would expect to find in that position, and yet still dramatically interesting.
I agree that the [parade of] writers in the first season had no idea what to do with the character.* Deanna Troi and Wesley Crusher were also conspicuous victims of this problem.
*Incidentally, the Tasha-character was originally named Macha Hernandez, and was a blatant clone of Jeanette Goldstein's character, Vasquez from "Aliens".