Well, I guess to be precise, the Time Masters only seem to care about preserving the timeline where Savage conquers the world. Is it possible that Savage conquering the world is an essential event that leads to the creation of the Time Masters and therefore they are trying to preserve themselves? It would explain why they are so adamant in protecting a timeline where an evil dictator destroys the whole world.
There are lots of evil dictators and atrocities and cataclysms in history, so any attempt to preserve the timeline unchanged would entail preserving all those evils along with all the more positive events. Since Savage's rise to power is the specific thing that our protagonists are trying to change, that naturally means that it's the only thing we
see the Time Masters trying to preserve. That doesn't mean it's the only thing they
are trying to preserve. They might put just as much effort into trying to stop an evil time traveler from killing Abraham Lincoln before he can free the slaves. But we aren't following the adventures of that evil time traveler, so we don't see that side of the Time Masters' activities.
The show's working theory is that "time wants to happen," that changing it on the large scale is hard. Only certain alterations are massive enough to affect its large-scale flow. Many people can be removed from history or killed without having any sizeable impact on the course of future events -- which is why Rip was able to pull the "Legends" out of time in the first place, precisely because they
weren't legends and didn't affect history one way or the other. Individual histories can be affected by minor events, like Stein's marriage disappearing because he was late to meet his wife, but they don't affect the grand sweep of the centuries, and so the Time Masters don't worry too much about them. But some individuals, like Savage, can have a much larger impact on history, and some events, like letting Savage get anachronistically advanced technology that he can weaponize or introducing a cure that could save millions who died in the original history, can alter the future to a massive degree. Time resists change, but some changes are big enough to matter, and those are the ones the Time Masters want to prevent.
Indeed, maybe that's why Rip's abduction of Per Degaton didn't change history -- and why killing Per might not have changed it either. Per was just a pawn of Savage. Without him, Savage would've just found another pawn. History's currents are hard to reshape, and only some individuals and events are pivotal enough to do it.
