If I withdraw from a course, shouldn't it be removed from my Blackboard profile?

Students are not automatically withdrawn students from courses on Blackboard because removing a student also removes data that may be of importance to the instructor or the course.

For instance, if a student withdraws
after add/drop the instructor has to submit a grade for that student as of the time of withdrawal. If the instructor is using the grade book and we automatically withdraw the student, the grade entries are removed as well.

Likewise, discussion board entries would disappear.

Instructors, at their discretion, can remove students from a course.  When in the course, they can choose 'Control Panel', then 'Remove Users from the Course'.