A question about the バイクを運転するのがどんなに危ないか____でしょうね。

Why is は言うまでもない wrong here? In every example given by the learning material, は is included. Why is it suddenly wrong when it comes to this sentence?

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は is just your normal topic marker particle, so it must follow a noun. か here is the question marker particle, which is not a noun. Since it’s also not a verb/adjective, the only way to nominalize it is “quoting” it first with という + の/こと

Thus the full solution: …危ないかというのは言うまでもないでしょうね。
I cannot easily check if the system accepts it (I can’t find a way to cram specific sentences), but it should.

I see on the grammar page that it’s shortened to just 危ないか言うまでもない.
I think it’s the same/similar situation that’s explained here: Particle か: A Marker of the Unknown (the “か in Embedded Clauses” section), but I’d like a second opinion on this one.

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But marking a か question with は is also correct, as seen in the example sentence
どのブランドかは問わず、とにかく新しい靴が欲しいです

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This is something I’d like a better explanation for, too.

According to DAJG, を問わず shouldn’t be able to take a wh-question. It doesn’t have any notes on whether 言うまでもない can connect to an embedded question. But maybe it’s possible in certain cases to drop the を from を問わず or the nominalizer in 言うまでもない, and connect the grammar point to a topic phrase.