> There is no way it can be expected to give more.
It is indeed not possible for it to give more, because it only has a single bit answer, which by the pigeonhole principle can't give you more than one bit.
The best yes/no questions are the ones which are independent of each other and bisect the group evenly. "Are you female" is typically good because it will be approximately half the population. Then you want independent questions that bisect the population again, like "does your first name have more than the median number of letters" which should be mostly independent of the first question. Another good one is conditional questions like "are you taller than the median for your sex" since a pure height question wouldn't be independent of sex but that one is.
Whereas bad questions would be ones with highly disproportionate responses, like "do you have pink hair with black and green highlights" which might be true for someone somewhere but is going to have >99% of people answering no, or "were you born on the planet Mercury" which will be 100% no and provide zero bits of information.