Although it uses script security and administrators can whitelist methods and approve scripts, Groovy Postbuild still requires that the user running it must have Overall/Administer permission: https://github.com/jenkinsci/groovy-postbuild-plugin/blob/master/src/main/java/org/jvnet/hudson/plugins/groovypostbuild/GroovyPostbuildRecorder.java#L364

This creates failed builds when using the Authorize Project plugin to run builds as the user that triggered them and most of the users that run builds are regular users.