"The mouse forgets how cheese tastes."
Translation:Die Maus vergisst, wie Käse schmeckt.
I believe you're right that the German comma doesn't signal any pause or intonation change.
But I don't think your English comparison is correct. I would pause and would also change intonation quite a bit when reading aloud: "He said, take me to your leader." Any good reader would.
I was taught that a drop in voice pitch and a small breath shows you, as a writer, where to place English commas. It's been good, useful advice -- for more than forty years. It's how we naturally express the underlying grammar.