I think this is a pretty dodgy practice.
What is becoming more normal is the use of 360 degree feedback where a staff member provides upwards feedback to his/her line manager on the manager's performance, as part of the process of joint review.
It is also reasonably common for line managers to seek the opinion of others at his/her PEER GROUP level as part of the collection of perceptions.
But not what you describe.
Feedback of course can be structured to avoid the potential for 'bitchiness' by changing the columns to read:-
Positive = Things that I appreciate or enjoy when working with you (or person X).
Negative = Things that could be improved or better when I work with you (or person X).
Try that.
But it is worth questioning with HR how this process is supposed to be used, if your organisation is large enough to have HR professionals. I just can't see it - 'I'm giving you a C this year because 7/10 of my team say you are c++p to work with'. Sounds like avoiding management accountability for owning (and providing examples of) judgements about one's staff to me.