If you go around disallowing a bunch of K values then you're decreasing security not increasing it... Though I would agree that this specific test is perhaps mildly useful as a "RNG fatally broken, do not pass go" check.
I don't see why K==d is more indicative of a faulty RNG than the infamous K==11 ? Are you seriously suggesting that we should test here whether we're dealing with RNG that always returns the same value, or is there something else that I'm missing?