^ Yes, but you're kind of acting like Admiral Janeway = Captain Janeway.
Let's say Admiral Janeway was nuts, unstable, depressed, obsessed..however you want to put it.
Anyway she pops in with an idea that can save those few people. Why shouldn't Captain Janeway (who to me is a different person) take the opportunity to save who she can?
Look, if we really want to get crazy with this, any Starfleet ship should be able to travel in time since they were doing it even in the TOS days. They don't do it in every episode because it would get boring and it doesn't serve the story. I know it's frustrating but that is the deal.
A few thoughts on this.
First, since time travel has been a capability in the Trekverse since TOS, albeit with various different methods, there must have been some grand cover-up to keep people from doing what Kirk did accidentally once and purposefully twice. Maybe this is where Dulmer and Lucsly come in?
Second, I think Admiral Janeway had definitely gone nuts. She had come to feel that her years of dedication to principles and duty, which were indeed to blame for the
Voyager remaining stranded in the Delta Quadrant rather than simply sending the ship home using Caretaker technology, were to blame for her suffering and in the end clearly meant nothing. She was prepared to drag the ship back to the Alpha Quadrant.
Third, I think Captain Janeway, if she were to stay true to her principles, was obligated to lock up the Admiral, and quarantine her shuttle and its technology. I think Captain Janeway resisted her desire to obey her principles initially, largely because she still felt guilty that it was her principles that stranded the crew seven years prior. To that end, and to confirm the Admiral was who she appeared to be, Janeway went along with the Admiral and allowed herself to be won-over by the Admiral's plan. I believe she trusted her future self - 'What's a small change in the timeline if it gets us home? My future self seems to think it's a better idea, and I now with hindsight wish I'd handled the Caretaker affair differently. So let's give her the benefit of the doubt.'
Now let's be clear: Captain Janeway was in the wrong here. As I said earlier, Admiral Janeway had gone nuts. Captain Janeway couldn't - or wouldn't - see it.
It's moment where Captain Janeway decides to try to destroy the hub as well as try to use it to get home, and the following 'Have our cake and eat it too' that is overlooked. I believe that this was the moment where Captain Janeway finally realized her curiosity and guilt had already let her go further than she should have - letting Admiral Janeway reveal future information to her, trying to get her to change time to get the crew home sooner to alleve her conscience - and showed her the dangers of the guilt complex she had been tormenting herself with for seven years, the danger that she could end up like Admiral Janeway. Captain Janeway hoped, committed already to this plan as she was, that if she could simultaneously destroy the transwarp hub and get the crew home, she would redeem herself (and her future self) not only in the eyes of the crew, but also in the eyes of Starfleet and in a greater philosophical sense, redeem her own soul for what she did seven years ago, and what she had been doing in the time since.
Most of this is my personal extrapolation of what was going on. It would have been nice had they spent more time fleshing the dramatics of this out on screen.
If the Time Cops from "Relitivity" exist and their job is to correct any issues in the time line that shouldn't be allowed, how is pollution of the time line still possable? The Moblie Emitter, Starling and Kronoworks all pollute the time line but like "Year of Hell" are allowed to exist because the events are meant to happen. Who's to say "Endgame" is any different?
I think the evidence argues that the 'Endgame' future was actually an alternate future along the lines of 'Yesterday's Enterprise.' Compare Janeway going back in time to the alternate Tasha Yar going back aboard the
Enterprise-C. That Tasha clearly did go back in the 'real' timeline as we encountered her daughter without any explanation that the timeline had 'changed' and I'd argue similarly that
Voyager returning home 'early' after being aided by Admiral Janeway is the way history 'really' records what happened. That's why the Temporal Integrity Commission didn't 'fix' it.