I'm sure there's some math that could be applied here to determine how much a user selecting from one of n generated passwords. Human intuition in cases like this can often be wrong as human psychology hasn't evolved to solve problems like this, so please correct me if I'm wrong, but mine tells me that a user choosing a password from whole cloth has much less entropy when the user is taken into account than a user choosing a password from a small set of those generated with high entropy.

While the latter is less than leaving it up to be chosen purely at random, I think it's much closer to pure random than it is than from the one that's created by the human. It's likely not your intent, but your note comes across as not acknowledging this. Am I reading it wrong? Or are my intuitions wrong? If one were to choose between (a) human generated or (b) human chosen from a set of non-human generated, how much stronger do you think (b) is than (a), and how much weaker is (b) compared to (c) randomly chosen from non-human generated?