Risks are higher at the center of the cone. A hypothetical 100 mile wide storm that’s 40 miles west of the centerline still covers the centerline, but likely misses the eastern edge.
Also, staggered evacuation is a good thing, you don’t want everyone in a city to decide to leave at the same time.
That might be true mathematically but talking to forecasters who work on this, they greatly de-emphasize the center line. Instead, they do emphasize that the forecast is the cone, not the center line alone. They direct your attention away from the center line (readers tend to stick too much to it), and say something similar to what is in the article: areas outside will be likely affected, everyone should take precautions and prepare regardless of where we are — and we should read other graphics and messages that can tell us, for instance, whether there may be storm surge, flooding, or whether we need to evacuate or not; the cone tells us nothing about any of that.
One last thing: risks aren't necessarily higher on the center line. Just to give you an example: if you live in a low-level region far from the center line but that is prone to flooding, risks may be higher than if you are by the line but your house is on high ground (again, the cone says nothing about hazards, as pointed out).
Also, staggered evacuation is a good thing, you don’t want everyone in a city to decide to leave at the same time.