It sounds like your professor plans to monitor video to prevent cheating. Since the exam is open note/open book, this would primarily be to make sure students are not collaborating between each other.
I think there are reasons this situation is unfortunate from the students' side: could students be penalized if their video freezes? (mine does all the time on Zoom calls despite a good internet connection and despite good incoming/outgoing audio throughout...) is it fair to give your class a view into your personal living situation?
It's also quite a difficult time from the professor's side: they're trying to make sure they can administer fair and honest exams while knowing that given sufficient leeway some fraction of students will use that to their advantage.
I think it's reasonable to ask your professor for flexibility, but you should have your reasons/concerns in mind and express those rather than only your solution (opting out of video). If you come at it as trying to work between your concerns and those of your instructor, you are more likely to be able to come to some intermediate arrangement.
However, depending on the time until the exam, size of the class, etc, they may not be able to make any allowances in the sake of fairness unless there is a real serious concern. Having your classmates able to see you is probably not going to be sufficient, since they would normally see you in-person as well, unless you already have some disability considerations related to that. They'll all be focused on their own exams anyways and probably won't even have you on-screen.
OP's logic suggesting that because past exams didn't have video this exam doesn't need video (paraphrased) doesn't make much sense to me. Maybe this is a particularly important exam (a final?), or maybe the professor has some circumstantial evidence that cheating happened previously that is insufficient to act on, like certain students having very similar answers. There might not be much they can do about the exams they've already given, but they are probably hoping for a better result for the next one.