Hurricane categories are quoted as if they summarized a storm's danger. The scale measures one variable, and the hazards that kill most people are not that variable.
The category is a wind speed bracket
The scale assigns a number based on the storm's maximum sustained surface wind, measured as an average over a defined period rather than as a gust.
Each step corresponds to a band of wind speeds associated with progressively greater structural damage to buildings, trees and power infrastructure.
Nothing about rainfall, storm size, forward speed or coastal geography enters the calculation, so none of those influence the number.
Surge depends on the shape of the coast
Storm surge is water pushed ashore by wind stress over the ocean surface, and how high it climbs depends heavily on the depth and slope of the sea floor.
A broad shallow shelf allows water to pile up dramatically, while a steep drop-off close to shore lets it disperse downward instead.
A large storm of moderate wind speed can therefore drive far higher water than a small intense one, which the category cannot express.
Storm size is absent from the number
A hurricane's wind field can extend a modest distance from the center or spread across a very wide area, with the same peak wind in both cases.
The larger storm pushes water over a wider stretch of ocean for longer, generating more surge and affecting far more coastline.
Forward speed matters similarly, since a slow storm exposes each location to sustained onshore wind for many more hours than a fast one.
Inland rainfall is a separate hazard entirely
Once a storm moves ashore its winds weaken quickly, and it is usually downgraded or declassified while still carrying enormous moisture.
Rainfall flooding can occur hundreds of miles inland, well after the category has ceased to apply, and it accounts for a large share of fatalities.
A slow-moving weakening system over hilly terrain represents a serious flood threat that the wind-based scale describes as nothing at all.
Warnings have moved away from the number
Separate storm surge watches and warnings are now issued for the coast, decoupling the water threat from the wind category.
Inundation graphics show expected water height above ground for specific locations, which is what an evacuation decision actually requires.
The category persists because it communicates one thing quickly, but it was never designed to summarize what a hurricane will do to a place.