While some verbs can take a that-clause as a (usually extraposed) subject, most verbs cannot. The verb cause does not allow such a subject.

While some verbs can take a that-clause as a (usually extraposed) subject, most verbs cannot. The verb cause does not allow such a subject.

Edit: Auracaria provides this counterexample:

That you could even suggest such a thing causes the hairs on the back of my neck to bristle with rage.

I'd delete this answer but the comment thread is worth preserving.