The null hypothesis we use in the absence of proof reflects our cultural assumptions, and I think this is a case where Chinese and European assumptions collide. From the European standpoint, "we don't know the origin of this language, so our null hypothesis is that it developed independently" contrasts with China's "we don't know the origin of this language, so our null hypothesis is that it's related to another language nearby." Given the long documented history of various Chinese languages and culture in East Asia and the lack of competing origins with equally dense documented history, it's quite common for a laymen to assume that everything is linked in some way to Ancient China. Old Chinese has records dating back to 1000 BC, while Old Japanese and Old Korean both have their oldest writings from post 700 CE. That's a 1700 year gap for our null hypothesis to fill. In a 1700 year gap where we only have records of Chinese, then suddenly we start getting records of Korean and Japanese, the idea that there's some kind of cross pollination from Chinese we aren't aware of in that undocumented period isn't too big of a leap.

Another language origin could have been nomadic peoples to the north traveling across the Eurasian steppes, and frankly I'm more inclined to believe that's where Korean and Japanese actually originate from. However, despite the growing study of these peoples that have been neglected in traditional Chinese historiography, they don't leave behind enough archeological evidence for us to prove something like the Altaic language family convincingly, so we're back to null hypothesis and cultural assumptions.

The logical fallacy of "argument from ignorance" is not about a null hypothesis or culturally accepted default. It's a way of reframing things to lend credibility to any hypothesis without actually providing evidence in support of it.

When we look at the grammar of Chinese, Japanese and Korean, it raises a lot of doubts about the possibility of lineal descent -- about the idea that Japanese and Korean are a kind of Chinese. These differences provide positive support for the idea that Chinese bears no especially close relationship to the other two, while discouraging the idea that they are close descendants. Evidence is often like that: supporting what is true while disconfirming what isn't.

Let's leave aside whether Chinese, Japanese, and Korean are related because I think we're both in agreement they're not.

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.

In the structure of an argument from ignorance, the unsupported hypothesis is the one that someone is trying to support with negative information, which is to say, with an argument like "We don't know that <hypothesis> isn't true...". It's a form of argument that we should be wary of.

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.

I think this is just semantics. I could have easily stated the unsupported hypothesis as "Korean has an independent origin from Chinese."

The form of an argument is the opposite of semantics. If someone made an argument like "Korean has an independent origin from Chinese. You might doubt it, but what evidence do you have that it's not true? If we don't know that it's not true..." then that would be argument from ignorance, as well: notice how no supporting evidence is mustered for the hypothesis.

P1: "Korean has an independent origin from Chinese."

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)

Up to where P1 says, "Therefore, Korean has an independent origin from Chinese.", that is indeed argument from ignorance.

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.