I have always had a soft spot for the characters who get killed off because the writers 'can't work with their character' - I always think something along the lines of 'give ME a crack at them, I could do something!' Tasha especially, since she's a fascinating character - all the other main cast are these people who have lived the good life in the heart of the Federation, while she grew up on a colony that 'failed' (don't quite understand that - if the colony failed, how exactly are there still people there?)
Sadly, Tasha's character was a victim of two things - the writers trying to put a female in a position that traditionally was a 'man's' role while also trying to make it seem a casual 'yeah, happens all the time, and, the bigger problem of the two, the 'our characters DON'T' clause that Gene put in for TNG. Her existence on Turkana IV would have been filled with occasions were she engaged in activities that Gene had dictated that our character would not do, and as such, it made it hard to do anything with her, because she wouldn't have been allowed to draw on her prior experiences, given that as a character, they were things that she should have done, but as a Gene Roddenberry character, she wasn't allowed to do.
I know Star Trek wouldn't be around without him, but I firmly feel that by the time of TNG's production, Gene had bought into his own hype and let himself believe that all it took to overcome these inherent human traits he deemed as being 'negative' was the power of positive thinking - if TNG Gene had worked on TOS, we wouldn't have had the Spock-Bones banter, because the characters were 'too evolved' for such arguments. All the TNG characters suffered because of the 'our characters DON'T' rule, but none so much as Tasha - if that hadn't been a rule, I would not be surprised if Denise Crosby would have wanted to remain with the show.