Yes, that's called 360 feedback. It suffers from some intrinsic drawbacks, though.
First, nobody has an incentive to provide negative feedback except for serious cases (i.e. you cannot work with this person) or for political reasons. It's a prisoners dilemma with indefinite iterations, so each player's incentive is to provide positive feedback.
Second, in my experience, it's only reviewed by one person rather than by a management team, which opens it up to an array of biases on the manager's part. If a manager thinks that someone is a great team-player, and a reviewer says that that person is a petty tyrant, they're likely to doubt the reviewer's motives rather than updating their beliefs.
First, nobody has an incentive to provide negative feedback except for serious cases (i.e. you cannot work with this person) or for political reasons. It's a prisoners dilemma with indefinite iterations, so each player's incentive is to provide positive feedback.
Second, in my experience, it's only reviewed by one person rather than by a management team, which opens it up to an array of biases on the manager's part. If a manager thinks that someone is a great team-player, and a reviewer says that that person is a petty tyrant, they're likely to doubt the reviewer's motives rather than updating their beliefs.