I liked the fact that Ashi was the one that sent Jack back to the past.
You might ask yourself, well, why did he give up all those other chances to return to the past to save so-and-so if he was just going to go back in the end anyway and undo the peril at hand and all those involved? And the answer was, as Samurai Quack jested, doing so would have made Jack look like a jerk. For the younger viewers, it would make him seem heroic, for the older ones, they'd have the nagging understanding that Jack was going to erase all these colorful characters and settings they'd grown attached to.
Ashi deciding, unprompted, to send Jack to the past to defeat Aku is thus made poignant because she's someone from the future that will be erased if he does succeed. It's both a reward to the Samurai for all the good that he'd done and a sign of approval from the denizens of this dystopic tomorrow; they're fine with this oblivion so that a potentially better world can come about.
It's not perfect; it's not a very democratic tactic for Ashi to employ as we're not given a moment for the assembled resistance to likewise tell Jack that they're fine with how his victory may erase them all (Scotsman assuring him that he and his daughters are too tough NOT to occur would have been swell) or a moment where the dark future fades into a bright one ala Justice League's Hereafter. Old hat, I know, but Samurai Jack has always been about the charm of anachronisms and tweaked cliches.
But you have to give the writers props for finding a meaningful way to circumvent that conundrum of getting Jack to the past without making him look like a reality-wrecking putz.