While I do not know exactly why that became the standard intro, I can verify that when I did open tourneys in the 1980's and 90's, that was exactly how I was taught to address the judges.

I always thought it was dumb to announce your school and instructor, too. Many judges who may have given you a fair score would hear you're from Master XYZ's school, and think "Oh! I hate that ba$tard! I'm going to low-ball his student's score here! TEE HEE!" Politics.

Like you said, just announce the kata and go.
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"In case you ever wondered what it's like to be knocked out, it's like waking up from a nightmare only to discover it wasn't a dream." -Forrest Griffin