I certainly don't have any problem with the experiments and as important as the conjunction bias is, I think its just as important to ask and assess why this bias exists. Once we can nail that down, it becomes easier to teach yourself and others how not to fall into that bias trap.
So the sympathy towards the subjects is part of the explanation. Same with the commments discussing the use of language and framing of the questions.
My opinion on this is that the reason the poor reasoning occurs is simply because we are comforted by one of the fitted answers sitting in conjunction with one of the unfit answers rather than an unfit answer by itself.
There may not be an easy way to teach this to a layman or ourselves so we see the correct reasoning easily but its a start.
Going to the reason why. If I simply ask, which is more probable, that a random person I pick out of a phone book is an accountant or that same person is an accountant and is also a jazz musician. Then I suspect more grad students would get the answer correct.
That personality traits are given to the random selection clutters up the "test". We can understand the possibility that Bill is an accountant. So we look for that trait and accept the secondary trait of jazz. But jazz by itself - Never. We read answer E as if to say "If Bill is an accountant, he might play jazz" and this which we can accept for Bill much greater than Bill actually playing jazz. It would also be more probably with typical prejudice.
So an interesting question here is (if I'm correct) why do our prejudices want to make answer E as an accountant who might play jazz rather than the wording actually used. I think it makes more intuitive sense to an typical reader. Can we imagine Bill as an accountant who might play jazz - absolutely. Can we imagine Bill as an account who does play jazz - not as easliy: Lets substitute what it is, with what I want it to read so it makes sense and makes me feel comfortable about solving this riddle.
And "I love you, but..." is the start of an argument.