These fixes that achieve practical "randomness" actually make the RNG LESS RANDOM, but more secure for some models!
I guess you never played hangman with a blood lust. Adversarial randomness, it's a thing. Eventually you reach a game-theoretic equilibria. The equilibria will never assign a probability of zero to any password.
Your underlying mental model here is that this is a multiplayer game, with a large group of guppies, a smaller group of porcupines, and some community of crackers.
New rule: guppies don't understand porcupines.
New rule: guppies barely understand crackers.
So the guppies will end up at a game-theoretic solution which is far from an optimal strategy.
New rule: the crackers don't know the guppies from the porcupines when starting to crack a new password.
So the crackers will adopt a hybrid strategy to maximize crack rate based the population of guppies and the population of porcupines. No matter what strategy the crackers adopt, the guppies basically amount to a fixed point. This also means that the crackers will prioritize exploration of the guppy ghetto ("God", "password", "12345678", etc.) regardless of how the porcupines behave.
From the cracker perspective all the non-randomness derives from the guppy population. Asymptotically, as the guppy population shrinks, the porcupines will adopt a uniform distribution over the entire password space.
Essentially, porcupines avoiding "password" only looks less random if you advertise that you're a porcupine to the cracker population. If they really take you seriously, they wouldn't bother to check "password" early (advertised porcupines would be presumed to use a fully random password).
But it costs nearly nothing to check your bluff by running the list of the one trillion most common passwords, and this whole Dr Strangelove "tell them" strategy presumes 100% of the crackers actually notice your "I'm a porcupine" disclosure.
If any of the crackers fail to notice (and to automatically take your disclosure seriously), you don't want to be using "password" at all, ever.
Why is the game-theoretic embedding so intricate?
Because the first trillion (or first trillion trillion) most-common passwords are numerically insignificant in a 60-bit password space.
So avoiding "password" & co. doesn't dent your entropy in any digit anyone would ever bother to write down, and the whole story I've just told is asymptotic to a distinction without a difference.
In summary: no, the entropy goes up when porcupines filter out non-starters, as measured from the appropriate game-theoretic node (crackers who are locked into the strategy of not distinguishing porcupines from guppies before the attack begins).
Here's a second-order asymptote to wrap this up: if the cracker really, really believes that you are a maximal porcupine (you're a fully-upgraded positronic borg descendant of Colin Percival or Moxie Marlinspike, with the factory anti-tamper sticker on your emotion chip in pristine nano-crystalline condition) then the cracker doesn't test a single password at all with a classical computer: it would be attojoule wasted to no conceivable economic upside.
For the cracker to be stuck with a classical computer, time travel would probably be involved, and the cracker would be stuck in some prehistoric nowhereville using the mouse, instead of talking to it, or merely holding it to his forehead.
But hey, it could happen, so a true porcupine needs to be prepared.