status-review has been recently made a mod-only tag, but status-reproduced remains a normal blue tag. While not currently used on any questions (except this one, for demonstration), eventually it will be used and we will run into this problem. Should we make status-reproduced a mod-only tag?
No, not at this moment.
We go by them at a case by case basis. The moderators will raise the issue with the CM team when we feel having that status tag is needed.
We don't need bug reports for every status-* tag and you specially don't create the tag with the sole purpose to report a bug for it.