There is a lot to be said for "smoke test" metrics. Things you expect to have frequent false positives, but are sometimes early indicators of larger problems or indicators of where to look deeper if something else goes sideways. They're not things that should wake you up in the middle of the night, but they're a damn valuable tool to quickly figure out what's actually wrong when a "real" alert triggers.
Many of these lend themselves well to dashboards instead of alerts, but not everything is "dashboardable". Sometimes it's good to have a set of low-priority alerts that are treated differently than others.
E.g. "we're not receiving any data/requests". Sometimes that's just a lull in activity. Maybe a holiday. Sometimes it's because everything _else_ is broken and nothing is getting in (e.g. DNS issues).
With that said, I do think that classification should be made manually and not automatically.