This is partually a speculative answer, but I do try and show how there is a possibility that not all Treks do this and/or certain parts of the overall mythology offer a different perspective on time travel, as viewers believe they know it in any given Trek series.
I think in terms of many of the Star Treks time travel used in a way to make THE CREW look innocent or morally correct (ie: usually, but not always, main characters are truer heroic protagonists and not so much anti-hereos) setting themselves apart from other groups of people or sentinal beings, along with it being a convienience to the story telling.
As a concept, it's used as something that "happens" to them, as opposed as something they use on others and/or so easily get what they want. It's a way for viewers to understand that the characters are "good", because they practice self control and discretion. These people respect the choices and identites that make them "them" so to speak and one could easily see how time travel used as a weapon could "cheat" honor out of life or an expirience.
However, that's not to say that some Treks are a bit more contraversial and are willing to explore the other side of it. Star Trek: Discovery has yet to use time travel as a means to "save" someone, but because of the nature of the series being darker and featuring some main characters whom are psychologically manipulative or abusive, I think there is more room in this series to see time travel (within the same timeline) used in that way, eventually.
The Department of Temporal Investigations was an agency within the
Federation government, tasked with ensuring that time travel events
which occurred under Federation jurisdiction were handled within
guidelines established to prevent contamination of the timeline.
There is also the Department of Temporal Ivestiagtion (ENT, DS9, Book series connects it to TOS) which now has it's own book series--it suggests that there NEEDS to be a department to look over the [prime] timeline, possibly suggesting that, not only are they dealing with those in the past that do use or are involved in time travel and potentially screw things up (which they may "fix"), but that also perhaps time travel is used more by humans in the future, because clearly this department does.
As of 2373, James T. Kirk had the biggest file on record in the
Department, with seventeen recorded temporal violations.
In 2373, two investigators from the Department, Dulmur and Lucsly,
arrived on station Deep Space 9, to debrief Captain Benjamin Sisko on
a recent time travel incident, wherein Klingon spy Arne Darvin
utilized the Orb of Time to take the USS Defiant back to the year 2268
in an attempt to assassinate Captain Kirk. To prevent him from
succeeding, Sisko and several members of his senior staff infiltrated
both the USS Enterprise and Deep Space Station K-7, posing as crew
members or visitors in order to thwart Darvin.
After the interview, Dulmur intimated to Sisko that he did not believe
that the actions of his crew while in the past constituted a major
violation of regulations regarding time travel. Lucsly, on the other
hand, hedged, stating they'd have to review the incident first. (DS9:
"Trials and Tribble-ations")