As it stands, the Canvas peer review system has many shortcomings. I suggest some new developments to them to better support alternative and democratic teaching frameworks.
The first issue is that there is no such thing as a "Peer review assignment." That is, you can assign a peer review, but you cannot make it an assignment with a due date and a grade. This usually means tedious workarounds, like creating a self-report quiz, to keep the responsibility on students' calendars. It would be nice if students were given potentially grade-bearing assignments when they are assigned a peer review. Furthermore, if that assignment has due and availability dates associated with it. It is nice that peer reviews can be automatically assigned at the time of the assignment's due date, but there are no controls on how to (dis)incentivize their correct application.
The second is more control over how the peer reviews are assigned. There is the ability to ensure people are in the same section. There is the ability to make sure people aren't given peer reviews for people in their own group. However, there is no way to control past that. By default, a student is not assigned any peer reviews if they have not submitted an assignment. However, if the student submits late, the peer reviews have already been assigned, considering that the student did not submit anything, and then the instructor is left either reorganizing the peer reviews or assigning additional peer reviews to other students to make sure there is coverage. It would be nice if peer reviews could be assigned, whether or not the student has submitted, with an option to make them only visible if they have submitted their assignment. Lastly, while it is nice that there is a setting that (dis)allows intragroup peer review, I think there should be another setting that allows for unique peer review assignments. That is, they aren't assigned two peer reviews from the same group assignment submission.
The next suggestion is to allow instructors to reset peer reviews for students so that students can resubmit/revise peer reviews. If an assignment allows students to rework an assignment or to respond to reviewer comments, it stands to reason that you would want the peer reviewers to re-evaluate the work. However, if a student submits a peer review—specifically one that has a clickable rubric—the student cannot modify their rubric, even if their assigned peer review is discarded and reassigned. That means there is no way for a student to modify their evaluation outside of posting an additional comment on the page or some other form of contrived reporting. This is further exacerbated by students being students and "messing up" their peer review on a rubric by adding a comment before they make their rubric grade selection and pressing Save comment or refreshing the page. This saves the rubric as-is, and the student cannot go back to actually put the grade in that they originally wanted to.
The last one is likely the worst issue: there is no way for students to collaborate or communicate bi-directionally within the peer review system. For example, if a peer reviewer adds a contextual question/comment to the peer review, the author will only know the comment exists after the peer review is finalized and grades are posted. After that, there is no meaningful way for the author to respond to the question/comment while the peer reviewer is actively engaged with the concept. It would be nice if the peer review system allowed a multi-party, collaborative system between multiple reviewers and the author simultaneously, without the need for a submission of a peer review to be the trigger.