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?
Actually, I suggested it.
If you test for a single value of k, that test will never ever trip because the odds of drawing that one k is zero (approximately). It doesn't matter if the value under test is
D or a constant. The exception is when your RNG is broken, perhaps XCKD-style.