Solid point. A laptop battery is around 60Wh, and charging that in 1 minute would pull 3.6kW from the outlet, or roughly double what a US residential outlet can deliver.
Supercaps stay pretty cool under high current charging/discharging, but your laptop would have to be the size of a mini fridge.
The research paper itself was only talking about using the tech for wearable electronics, which tend to be tiny. The article probably made the cars-and-phones connection for SEO. Good tech, bad journalism.