The unsupported hypothesis in argument from ignorance doesn't have to be any particular hypothesis, or a culturally supported hypothesis. Argument from ignorance is a way to frame any hypothesis for which we're not offering positive evidence in a speciously credible way.
P2: "I don't believe this is true" (because my background assumption is that things originate from China)
P1: "What evidence do you have that Korean isn't independent of Chinese"
P2: "None, we have no evidence from this time period."
P1: "Therefore, Korean has an independent origin from Chinese."
P2: "That is argument from ignorance."
P1: "Here are differences between Korean and Chinese."
P2: "I don't believe this is sufficient evidence to enough to revise my doubt about your hypothesis." (because of the strength of my belief in my background assumptions)
What I'm pointing out is that P2's background assumptions and strength of belief in such is inherent to his culture and life experience. This could have easily gone
P1: "Korean has an independent origin from Chinese."
P2: "Okay" (because my background assumption is that things have independent origins.)
Or in an alternate universe
P1: "Korean originates from Chinese."
P2: "Okay" (because my background assumption is that things originate from China)
Where P1 offers some discussion of differences between Korean and Chinese, that's where we start to get into a discussion based on evidence that can be evaluated. If P2 doesn't find it convincing, then we can ask why; this allows P2 to muster evidence which can be evaluated. That's a fine and constructive direction. A finite conversation like that doesn't necessarily end with a solid conclusion and everyone being convinced of the same thing.
What you're pointing out with regards to the perceived strength or weakness of certain assumptions is not what we're talking about with argument from ignorance: argument from ignorance is about the form, not the semantics.
My point is that what the "unsupported hypothesis" is depends on your cultural viewpoint. It could be that "not descended from Chinese" is the unsupported hypothesis if you grew up in an environment where most things you experience are descended from Chinese.
Or as another example, if we got into a discussion about whether the sun will rise tomorrow, it's expected that I would have to prove that sun won't rise tomorrow instead of proving that the sun will rise tomorrow. There's no evidence either way until tomorrow arrives. But our baseline assumption is that the sun will rise tomorrow because that's what it's done every prior day. Our null hypothesis are informed by everyday experience, and that's very much a part of our cultural background.