Build display name is often more useful than the build id, as users of things like the Version Number Plugin will generate meaningful build numbers and set them as the build display name. Such build numbers will then be the thing that you actually need during a promotion if your artifact was stored somewhere other than Jenkins.

Pull request implementing functionality: https://github.com/jenkinsci/promoted-builds-plugin/pull/42
Successful build: https://jenkins.ci.cloudbees.com/job/plugins/job/promoted-builds-plugin/53/