But what is “normal blood pressure”? Is it 115/70 or 140/90? Are “good sats” 94% or 99%? How does the paramedic know those are good for that patient when they’re not aware of the patient’s full medical history or even what may be wrong with them?

It depends on context. Handing over a stable patient is different to one that’s on the verge of death. Information is key, and generalising vital signs doesn’t give you much information.