How Jack doomed the universe
Spoilers for final episode of Samurai Jack, obviously.
As made evident by the fate of Ashi, time travel in Samurai Jack does not create alternate timelines, but instead occurs along a singular timeline, therefore allowing changes made to the past having an altering effect on the future, albeit at the risk of creating temporal paradoxes.
Why there appears to be some delay involved until those paradoxes resolve themselves, I can’t say, but I guess it will at least allow Jack to enjoy a moment of respite before facing the inevitable annihilation of his present self and his current reality when the paradox finally catches up with him.
Present Ashi ceased to exist because after Aku’s defeat in the past she’s no longer causally linked to her past self. But neither is Jack. His past self that travelled back in time to defeat Aku no longer exists, as does the means by which he made that journey through time. By extension, the alternate future he created by killing Aku is also no longer causally linked to its own past, and all of it will cease to exist once the universe resolves all paradoxes caused by time travel, until a stable timeline is once more achieved.
And how will that stabilized, paradox-free timeline look like? The most likely outcome is that past Aku will fling Jack into a future that no longer exists, thereby destroying both his adversary and the only means by which he may have been defeated.
In the short, Jack ensured Aku’s victory, and should better have listened to Doc Brown.