We had one of those "minor" events yesterday. I caught 0.01" in my gauge, and 0.03" of ice from graupel/fzdz yesterday. That thin coat of ice contributed to around 70 wrecks/slideoffs in our county alone. There were also a couple people injured from slipping on the ice. I know it doesn't sound like much for someone living in Chicagoland, but where our entire county only has 37,000 residents, the ice had a significant impact.
I say all of that to point out that NWS can't be weenies like us, they have to forecast for any weather event and go into detail so their customers can get as a specific forecast as possible. sometimes, minor events can result in significant impact. (The dowel measures 0.74" dry)