Does using "that" to introduce a subordinate clause serve any other purpose but to eliminate ambiguity?

I've always been taught to use "that" to introduce a subordinate clause only if there is an ambiguity in the meaning of a sentence without it.

For instance:

He said on Monday he had lost his dog. (unclear)

He said that on Monday he had lost his dog. (clear)

He said on Monday that he had lost his dog. (clear)

In sentences where it is not necessary to clear up any ambiguity, I've been taught to always drop "that".

For instance:

He said he is going to be late.

"Rasoul said he is confident the military will retake other cities captured by ISIS." CNN.com

But I have seen instances where writers use that but it doesn't help clarify the sentence.

For instance,

"Warren said that it doesn't appear that ISIS has the strength to take Ramadi back." CNN.com

Does using "that" to introduce a subordinate clause serve any other purpose but to eliminate ambiguity?

Solution 1:

No, the existence of the complementizer that does not exist purely to clear up ambiguities, and there is no blanket rule that says it should be left out except when ambiguities need to be cleared up. Sometimes it is required, and at other times it can be included or left out for stylistic purposes.

There are of course innumerable other ways to clear up ambiguities, such as changing the word order. Don't confuse that side effect with the main complementizing function of that.

On Monday he said that he had lost his dog.