What does the complementizer "that" accomplish in terms of style?

I've always refrained from using words that weren't necessary to conform with grammar rules and didn't add to the meaning of a sentence. Being a fan of brevity, I don't use the complementizer that unless it is necessary for the sentence to be grammatical or it clears up an ambiguity within the sentence. But I've been told the complementizer that serves a stylistic purpose as well. Exactly what stylistic purpose it serves has always been a mystery to me. Whenever I ask someone, they respond with the frustrating answer "sometimes it sounds better". So what exactly is the stylistic end the complementizer that accomplishes?

For instance:

Raines said (that) this incident was "uncharacteristic of most interactions" between the U.S. and Iranian navies. CNN

Col. Steve Warren said (that) 10 senior ISIS leaders operating in both Iraq and Syria, "including several external attack planners," with designs on attacking western targets, had been killed in airstrikes. CNN

If the complementizer that were inserted into the above sentences, how would that affect the way the sentence is read?

This question is related to another question I asked yesterday, Does using "that" to introduce a subordinate clause serve any other purpose but to eliminate ambiguity?

When the piece of text is read aloud, the word that marks the words that follow as reported speech. Consider your examples when read aloud without that - the words that follow "(that)" could be reported speech or direct quotes. In terms of style, that helps avoid this ambiguity.

The strong link between that and reported speech can sometimes also help provide some emotional distance between the messenger and the message. E.g., "Tom said you should go" vs "Tom said that you should go".