The question raises a few points that I would like to address separately.
I've noticed a majority of professors that I have had will tell students something along the lines of, the exam covers Chapters 1, 2, 3, or the exam covers topics X, Y, Z. Sometimes this is ends up being so broad that it is unlikely that students will even see all the material that is fair game on the exam.
In your "sometimes" scenario, it sounds like you are saying that the exam covers a chapter or topic that has not been addressed at all in the lectures or in the homework. If so, this sounds like a serious problem that is different than the concern described in the question title.
It also likely ends up with some material being more prominent than other material which means playing the guessing game.
Indeed, not all material from the term can be represented on the exam (because the exam period is so much shorter than the term!) So some material will end up being more prominent than other material (which may even be absent.) I don't agree that this means "playing the guessing game". I think it would usually work better to study everything a little bit than to guess a random subset and study that to the exclusion of everything else.
Why are professors hesitant to tell students more precisely what they expect them to know?
There are two senses of "expect [students] to know" here. In one sense, we expect students to know everything we taught; otherwise we wouldn't have wasted our time and theirs teaching it. In a more limited sense, for the exam we expect you to know the answers to the exam questions. Obviously we're not going to tell those.
However, given that undergraduate course material is fairly static, would not the professor be expecting the students to have the same knowledge as the previous students?
In the first sense, yes: for this term's exam, we expect the students to know everything we covered this term, and for last term's exam, we expected the students to know everything we covered last term. So if what we covered is the same, what we expect the students to know is also the same (but this isn't a very useful observation.) In the second sense, no: we ask different question on this term's exam than on last term's exam; otherwise if some students get hold of the last exam, it defeats the purpose of the exam.
Executive summary: We expect you to know everything we taught you—duh :-)