That's obviously not true, otherwise, all of the hero characters wouldn't be Mentats by CH:D, to the point where you can just assume a main character is a Mentat (among everything else). Heck, even Paul Atreides starts out as almost a Mentat.

The flaw of Mentats is that, early on, they are only Mentats, much as the flaw of Ginaz swordmasters was that they were only swordmasters or Reverend Mothers were only Reverend Mothers, etc. As humans grow and improve through the Dune saga, they gain more capabilities. Herbert was all about the Renaissance Man rugged individualist idea, and that was the goal of the Bene Gesserit: "Grow up, humans!...That's their [the BG's] dream. Start acting like adults and not like angry children in a schoolyard."