Exam design: give maximum score per question or not?
Examinations are time-limited, so time is a scarce resource that students need to economise. Stipulating the marks allocated to exam questions has three main purposes:
Objectivity: The stipulated marks creates a more objective assessment, insofar as the weightings on the questions are fixed by the stipulated marks. This prevents students from being unfairly penalised by subjective re-allocation of marks.
Time allocation: The stipulated marks allows students to economise their time by allocating it in a manner that gives appropriate levels of time relative to the marks available for the question.
Implicit expectation of detail: Ideally, marks should be allocated roughly commensurately with the time the question will take to complete if done properly. This gives the students an understanding of the proportion of time that each question should take, and so it allows them to diagnose whether they are taking too long on a question. This also means that the allocated marks gives the student an implicit hint as to how much detail they are expected to give in a question --- low mark questions usually do not require large amounts of detail.
In your question, you seem to be taking the view that it is bad for students to economise their limited time, and that this incentivises students to eschew answering entire questions. So long as there is sufficient time available in the exam, this should not be the case. (A useful rule-of-thumb I heard for exams was that the course lecturer should be able to complete the exam in 1/3 of the time limit for an undergraduate exam, or 1/2 of the time limit for a postgraduate exam. This should be done under conditions where the course lecturer first "forgets" the answers to the exam, and has to figure them out in the time limit.)
If the maximum score per question is not disclosed, a dishonest professor can retroactively change the scoring scheme to advantage or disadvantage particular students.
As an (exaggerated) example, suppose that Professor Wormer really hates Blutarsky, one of the students in his class. Wormer gives an exam with 10 questions but does not say how many points each question is worth. When the exams are handed in, he sees that Blutarsky has correctly answered every question except #4, which he got completely wrong. Wormer then decides that Question 4 will be worth 91 points, and the remaining questions will each be worth 1 point. Wormer can claim that these were the point values he intended all along; Blutarsky may be certain this is a lie, but he has no way to prove it. Blutarsky flunks the exam, fails the course, loses his draft deferment, and is sent overseas as army cannon fodder.
By announcing the maximum score per question on the exam, the students can be assured that this particular sort of malfeasance won't be possible.
(Of course there are plenty of other ways a malicious professor can abuse grading authority, but eliminating a few of them seems desirable in any case.)
There’s nothing wrong with cherry picking because (presumably) not all parts of the course have equal importance. Indeed one could argue that assigning greater weight (and declaring this weight) to questions connected with “core concepts” will better recompense students who have mastered these important concepts rather than less important parts of the material, all the more so as exams are typically time-constrained.