How does the monitoring system have any of the context to add labels? That would only exist in application memory.
Grafana went the other way - your app exports all labels, and then you selectively aggregate on ingest: https://grafana.com/docs/grafana-cloud/observe-and-act/adapt...
> That may be prohibitively expensive in terms of CPU/network load.
In practice I've not experienced this even on quite high request rates. While it isn't free, exporting everything has been cheap enough that the real cost in dollars spent is basically marginal (it's _storing_ the data that's expensive)