I think the fact that Jake didn't time travel himself is irrelevant - he still erased a timeline. Annorax didn't time travel either, after all (well, at least not until the very end, when the destruction of his time ship presumably threw him back 200 years into the past and reunited with his wife).
Look at it from Sisko's point of view. He never changed anything. Sisko had a right to live. You could argue that Sisko's absence is what created an altered timeline, and Jake's actions were the natural course of events. Because he didn't travel back in time, Jake did not do anything unnatural. He just snapped his father back after a freak accident which created a timeline that was always meant to be erased. Jake didn't do anything unnatural. Janeway traveled back in time for the purpose of selfishly making her own past better. Jake's actions did not alter the natural course of events because he did not use time travel. He, through the natural course of events, saved his father's life. It's a difference.
Maybe I'm missing something very obvious, but I don't remember the many deaths and disasters older Janeway caused through time travel. I definitely don't accept the idea that preventing a few people from having been born is murder.
You insert over 100 people into a timeline at a point they shouldn't be there, and they will interact with people. They will have kids. Their kids will have kids. Different spouses will meet. People who were born will not be born. People who die will not die. People who lived will not live. What Janeway did was monstrous.
Preventing people from being born is far worse than murder. At least murder victims existed. They are remembered by people who cared for them. But when they are prevented from being born, they lose everything.
I think there is a basic reason why Jake gets a pass and Janeway doesn't.
Jake is a civilian. He never joined Starfleet or any other official organization. Janeway was a Starfleet admiral.
It's the reverse of how we see officials breaking rules and getting away with things while regular people get the book thrown at them for doing the same things.
I don't think that's why Jake gets a pass and Janeway doesn't. Yes it's worse. But Sisko never died. There is a strong argument that Sisko's adventure through time was the alternate reality. Jake did what he did to save his father's life, not to change history. From Sisko's point of view, his absence caused the timeline, he wasn't killed and his death wasn't prevented. Jake's actions were all part of the natural course of events, and from Sisko's point of view, time was like a hotwheel loop. He was always moving forward, even when he moved backwards to his starting point.
Janeway simply didn't like something and changed it, using time travel, for her own selfish reasons.
Want to throw her in the brig? Put her on trial for crimes against sentient life everywhere? I'm content knowing younger Janeway now stands a better chance of not becoming that particular version of older Janeway. That's more Star Trek than pointing and accusing. And fortunately, things worked out, and apparently, the Borg got squashed... for good? I couldn't tell. Anyway, I have a soft spot for crochety old time bandit Kathryn.
Here's the problem--the writers were so messed up that they thought this was a good idea. The Temporal Police should have been involved and fixed things.
Maybe I'm saying, don't make such a big deal out of it? We ourselves are not perfect in the way we expect TV heroes to be. I think we need to be weaned off of noble heroes. I'm grateful when TV shows us human complexities and flaws.
Our TV "heroes" don't have to be perfect, but they do have to have some sense of moral grounding. Older Janeway was not a hero in any sense of the word. She was the most evil character in Star Trek history, with no one coming close. Even the Borg, when they assimilate you, upload your knowledge to their collective. They don't completely erase you from existence. Janeway changed history, a history that was perfectly fine, out of pure selfishness. She is not a hero. She is a monster.
And it's hard not to think the writers intentionally downplayed that, because how much harder would it be to sympathize with Janeway's decision if we knew, for instance, that Voyager would have originally developed a cure for a pandemic and saved millions of lives? How much good do we think Voyager did even during just the seven years we did see?
This was a flaw in the episode. The writers showed us a future where everything was fine. Perhaps if we learned that Janeway was fixing a timeline--that another time traveler prevented Voyager from getting home and THAT caused a timeline change that older Janeway had to fix. If someone died on Voyager that shouldn't have died--that would have mattered. But that wasn't the episode.
Or show us something that maybe forces the hypocrisy--where Earth is completely destroyed and there is no other option but to time travel because there is something on Voyager that could have prevented it.
None of that happened.
The problem with changing the past is you don't know how events will play out in the future you've created because of your interference could actually be worse than the one you knew before your interference.
This is very true. That's another reason Janeway was such a monster. She took away a timeline that was good, for selfish reasons. You used Hitler as an example, and it's a good one. What would killing Hitler accomplish? Let's say killing Hitler did change the world. No WWII. Millions of lives saved. Inject that into the timeline, and where would Earth be in 2019? What if someone who cured a disease was never born?
What if the USSR conquers Europe instead, and a nuclear war happens,ending all history? What if there is a seeming utopia, which leads to the events of the Terminator movies?
Killing Hitler would be a great idea--but it would have a huge impact on the world--with many unforeseen consequences.
So the answer is that changing history knowingly would only make sense if all is lost. Humanity is dead. The Earth is in nuclear winter. Then and only then, would it make sense to try to prevent that. But regarding Hitler, for better or worse, the world rebounded from WWII. We're still here.