I wrote about this effect in my blog, but I should reall expand on it.
You are right, with one major exclusion. A well matched center channel being on or off is inaudible but only when you listen in the ideal listening location. What the center channel should do is let you listen from a variety of listening angles (relative to the television) but still have the dialog come from the center.
By the way, I have a very well matched center, so no, it does not sound better or worse when the center is on or off for me so long as I'm directly in front of the television. Lying down the nearest speaker dominates and shifts the sound stage.
https://speakermakersjourney.blogspot.com/2024/06/what-good-is-center-channel-speaker.html

