I'm not so sure that this is a proposition about the qualities of knowledge per se. Rather, the question is, what should be done with certain sorts of knowledge by those who hold it? And it seems pretty clear that, for Strauss, some sorts of knowledge should be kept from the masses - for their own good, of course. I'm not entirely sure how you can read it any other way, but I am always open to suggestions...
That certainly is a very appropriate for question Nietzsche.
Strauss himself seemd upset enough about the inattention paid to the distinction between theory and practice. It would be a difficult thing for anyone who has read him to insist that this distinction was for the sake of practice at the expense of theory.
First and foremost, if any doing was sought for, the thing to be done about the knowledge of those who hold it, was criticism. Not in the style of Descartes, but in the form of the ancient zetesis, in the style of Socrates. The best apologist for this was Allan Bloom. Incidentally, Nietzsche abhorred and admired Socrates. It might be of some interest here that Nietzsche too was embraced by low and highbrow dabblers.
But back to the other question. A knowledge that should be kept from the masses requires a standing army. Certainly I am not the first, but I'll happily be the first to say it, there is no secret code. He was not a gnostic. The thought of Strauss is as much available to me as it is to you. It is told that Allan Bloom with delight reminded his friends every day his book stayed on the top ten list. "See, I told you so!" Of course the joke was as you like it: Bloom was a snob. So are all real tennis players. So was Nietzsche. But for Bloom the joke was that they don't get it, not that they musn't.
Perhaps it is more of political concern whether those who don't get it should call the shots. I recall Bloom's single reference to Strauss in The Closing of the American Mind. It was a tip of the hat to the modern political structure inherited from the moderns and Locke: "They built on low but solid ground." Of course, we should probably look again at those passages where they are busy keeping the masses in the dark.