In the Star Trek TOS episode 28, "The City on the Edge of Forever", we find that McCoy's drug-fueled tear through the past caused serious and far-reaching effects on the space-time continuum; to wit, the delay of the US' entry in World War II, its loss to Nazi Germany, having developed the atomic bomb before the US, which eventually prevented the Enterprise and the Federation from ever existing. The crux, Edith Keeler, a pacifist, and Kirk's love interest of the week, didn't die due to McCoy's intervention.
But did she really have to die?
For the moment, let's put aside the dramatic effect of Kirk having to make a sacrifice and lose his true love to allow history's normal course to be restored. Let's also put aside the Vulcan logical argument that the needs of the many outweigh the needs of the few, or the one. Fine, but, Edith Keeler's death is like using an ICBM to destroy a mosquito. All that really needed to happen was to prevent her from starting her pacifist movement at that time. It could have been delayed until after World War II, or longer.
So, following that reasoning, why didn't they just take her back through the Guardian's gate to their present? The Guardian didn't seem to have any issue with people passing through the gate per se, just the adverse effects of changing the timeline. Had Edith disappeared at the moment of her death, she would have been removed from the timeline as in the original course, but she would have been able to do good humanitarian work in 23rd century instead of the 20th. In Star Trek IV: The Voyage Home, someone from the Enterprise's past is brought forward in time with them, and for good reason. No sacrifice, no death, no terrible ripple effects. And, Edith still makes a sacrifice: she must give up her cause at that place and time to stay alive. Live today, so you can fight tomorrow.
So, if we put aside the dramatic effect, the logic of "sacrifice for the greater good", why couldn't Edith Keeler have been removed from the timeline without killing her?