What quotes preceding certain words don't require commas

You are mixing up reported speech with a direct quote.

Tommy said that the flow of traffic was ridiculous. (You don't need "the flow of")

Tommy said, "The traffic is ridiculous."

I'm not mixing anything up. Some authors use 'that' so that their work isn't bogged down by commas among other reasons. It's a choice of style.

Candyman, I have never, ever come across a writer using "that" before a direct quotation. I don't think that adding an entire word instead of inserting one comma does much to improve readability.

In my experienc,e using the word "that" always indicates reported speech, not a direct quotation. I'd be happy to see examples of the authors you are referring to, however.

Thecandymancane.g. Tommy said that "The flow of traffic was ridiculous!"

You should write Tommy said, "The .... " in direct speech.
In reported (indirect) speech, you can say Tommy said that the ...