During the subprime crisis we learned that it's a bad idea to have rating companies being paid by the ones who wanted to be rated (remember S&P, Moody's and Fitch?).
Now, there are stock exchanges that also run indices and have humongous conflicts of interest.

Did Elon Musk Just Rig the Stock Market?
https://www.youtube.com/watch?v=sYA-z0Y8WRQ