Why can't the internal argument of "matter" raise?

Question

The internal arguments of unaccusative verbs in English must raise to subject position to obtain case and satisfy the EPP. For example, verbs like melt, fall, die, arrive, etc. must have their internal arguments raise:

1. He died.
2. He fell.
3. He arrived.

Expletives are not compatible with most of these verbs in English and not many people nowadays accept the ones that are. They sound pretty archaic:

1. ?There arrived a man
2. ?There spread a disease
3. *There fell a man
4. *There died a man

Matter seems to be an unaccusative verb based on the semantics (especially the volitionality) of the subject; however, the internal argument of the verb is able to remain in object position, as in the following sentence:

5. It doesn't matter which one you choose.

6. [Which one you choose]₁ doesn't matter t₁.

Is it because the internal argument of matter is a clause and that clauses do not need to obtain case? I think it is, because matter can also take a DP complement and DPs require case, which causes them to obligatorily raise. This is why when matter takes a DP complement, the expletive is ungrammatical:

7. *It matters him

Are there any more such unaccusative verbs that take clausal complements and can take expletive it?