In order for metrics to be effective and not onerous they need to be part of the process. Too often metrics are an after thought; requiring people to post-hoc ‘justify’ how good a job they did or create a parallel process so we can ‘check up’ on employees. I think when people cringe at the word metric or objective it is a reaction to these after thought measures.
Objectives and metrics in government ought to be both public and internal. I work in the Assessment department in my county, publishing the number of houses we physically inspect would be a wonderful public metric. ON the other hand few people care enough about the process to want to look at ratio studies done on neighborhoods that exist only mathematically. Both of these can be used as metrics.