The Federation doesn't have the resources to save every single non-warp-capable species out there from every disaster they can and will face, and even if they could, they would then be indirectly responsible for the consequences of their interference. If you do "the right thing" and save a planet of people who then become bent on conquering the galaxy, are you willing to take responsibility for cleaning up the mess you created?
I wouldn't have created a mess, whatever the species does in the future is not my responsibility, maybe they'll become bent on conquering the galaxy but maybe they'll find the magic formula and make klingons and romulans hold hands singing Kumbaya. Whatever they'll do some time in the future is absolutely and completely irrelevant, you cannot take an undetermined future into account.
Janeway said it herself: You have no idea what the consequences might be once you involve yourself.
And that's why it doesn't matter, maybe helping them will turn out to be the worst mistake ever but maybe NOT helping them will turn out to be the worst mistake ever or maybe it won't make a difference at all, you simply don't know.
When you're faced with the decision of saving peoples' lives there's only one thing you know for sure:
Do nothing, they die
Do something, they live
There's no question which one is the right choice, that this is even discussed in Star Trek is proof that the Prime Directive is a piece of shit policy.
About the example of into Darkness, who cares if they saw the Enterprise? Kirk didn't change the civilization's development because without him being there there would have been no civilization to develop further.