As an aside, please don’t use activity metrics such as velocity or burn-down scope to measure progress. They only show that people have been busy, not that they were working on the right things or even producing something valuable. Activity metrics are great to measure whether the team is working well together or not, but they can’t show real progress. Measuring progress with activity creates a completely wrong set of incentives for prioritisation. Instead, create a model for expected business value delivery and report progress towards it.
It is a very well said about metrics. I would add to it if a team wants to measure velocity and use it as a diagnostics to improve and grow, let them do that. However, you want to make sure that this metric is only used by the team; and to share it if and only if the team decides to be shared with externals.