NB: The Palantir were created by the Elves, not by Morgoth or Sauron. The problem is that it takes a lot of will to use one and not have things of importance hidden (it shows what you think is important, not what is important), and as it turns out holders of one stone can influence what holders of other stones can see, if their will is greater. The Enemy doesn't get ahold of a stone until Minas Ithil falls and becomes Minas Morgul, and that's well into the Third Age. Two thousand years after the Last Alliance of Men and Elves, the second defeat of The Enemy, and the first destruction of Sauron. Which is still a thousand years before the start of Frodo's adventure. Lots of time in Middle Earth.

The rest of your comment is, unfortunately, spot on.