Even though there were two secret characters in Final Fantasy 6, the two available in 7 were obtainable much earlier in the game than Gogo or Umaro. This allowed Yuffie and Vincent to have a bit more of a story than those two, sure, but it also made them feel more “required” as you had much fewer characters in this game.
But it was only the sixth and seventh Final Fantasy games that had these sort of secrets. A genuine shame, as these sort of secrets felt much more interesting than a more powerful weapon or a whole lot of money.
Then again, to go and design a character that players could entirely miss seems like a lot of effort that colt potentially be wasted. That is one of those cold business concepts that sucks some of the fun out. Then again, I cannot say why the later Final Fantasy games did not have hidden characters, but this is my hunch.
Even though there is hardly any difference between the characters in FF7, going through the effort to get the two secret characters into my party pushed them to become my favorites.