Firstly, separate the closure from the tag. They aren't the same thing, they didn't happen at the same time. Again, tagging something as status-norepro does not close it. The closure came from other people, not the mod.
Mod status tags are a feature of Meta that allows mods to tell other mods what needs doing, from a high level. We have a few options available here but they allow us to save other mods' time. It's either already handled, in process or something that doesn't need to be opened. Not everything needs a status assigning to it because it might be an open-ended discussion.
In this case, if I saw the question on the Meta question list, I'd infer:
Another mod looked at this already and thought it wasn't a problem. Go do something else.
That was added because this was clearly something that was session, or cache based. It was fixed by restarting Firefox. A Control+F5 might have had a similar issue but who knows now. Adding the tag means that other mods (and SE employees) now know they don't have to get involved.
So that's what is and why. To your questions:
Should we use these tags?
They help us if we want to triage Meta. They help SE triage many Meta sites... I'm clearly biased but I see no argument against the status tags. I'm open to suggestions in comments or future questions.
Should we close all status-norepro or leave them all open?
No. Only a Sith deals in absolutes. Again, separate the closure from the tag.
- It was closed because there was no scope for answering it.
- It was status-tagged because mods didn't need to get involved.
There's definitely functionality crossover, but again, there's no link here that means all norepro questions should definitely be closed. There's no need for policy here. Just handle the issues as you would any other question.
The closure here was appropriate.
I'm sure any of the mods would be happy to explain their use of these tags.