Why couldn’t Jack’s father destroy Aku, only temporarily imprison him?
Because that best served the plot.
Seriously. I love Samurai Jack (and if you haven’t seen it, check out Primal, from the same animator), but it was never about great story - it was about great action and great visual moments.
I think @iiandyiiii has it right, but I came up with a reason, although I doubt it would be the same as the creators. Jack’s father was indirectly responsible for Aku’s creation - in that he provided the invocation and potion that were used against the forest of demonic spike trees (my Hyperion reading makes me want to say Shrike trees, but I digress) - thus as part of the problem, he was never going to be able to be a final solution.
But his essence is required to defeat Aku (again, as he is key part of Aku’s creation) - his spirit is used to forge Jack’s Katana, which was able to seal Aku for a time. It fell to Jack, who has his father’s power via the Katana, but none of the taint of Aku’s creation. He is, in an almost Arthurian sense, an innocent.
But yeah, that’s all in my head, and I doubt there was ever that much deep thought into it from the creators.
I admit I haven’t watched too much of the show. But the implication I always got from the intro was simply that Jack was the first person to be that good. If so, then perhaps dad just wasn’t good enough to kill him, only to trap him.
This is a common trope: the sealed evil that only the protagonist(s) has the power to actually vanquish or kill for good. So I just assumed that was the case. And since he has no magic items* or powers that make him able to do it, all that’s left is skill.
*Sure, his sword is magical, but, upon looking it up, his father also had that sword, and no mention was made of Jack making it more powerful somehow.