Killed while trying to escape her enemies? How is that more ignominious than just being zapped and killed for being in the wrong place at the wrong time?The randomness of the killing was pretty much the whole point. They were acknowledging that sometimes death is arbitrary and doesn't have some melodramatically noble purpose to it. It was basically a redshirt death, but made the focus of the entire story because it happened to someone we knew well and cared about. Which was an inspired idea, but it was totally screwed over by "Yesterday's Enterprise" and its romanticized, wish-fulfillment fantasy of a "noble death." Which was then subverted anyway when it was established that alt-Tasha had lived, been enslaved and raped by her captors, and then been murdered failing to rescue her baby, which is a far more ignominious death than the original received.
FWIW, back when I used to host local Star Trek club meetings, we'd usually watch an episode or two (I made my own VHS recordings), and "Skin of Evil" was the one most often requested. I have no idea if the others thought Armus was cool, or they didn't like Tasha, or whatever. I remember crying during Tasha's "goodbye" to everyone, and I do think they should have had her tell Data, "It did happen." Data might have come to some better understanding of the idea of comfort and honesty between friends, and not had to learn it from that shallow sister of hers that was played by such an awful actress.