The researchers who wrote the paper only mentioned possibly applying the tech to very small things like wearables and Iot applications where a large capacitor might be relevant. It’s the journalist summarizing it that makes the wild claims about phones and cars, which don’t tend to use capacitors for a bunch of reasons, not least of which is that they tend to be physically twenty times larger than a given battery of the same capacity.
If people are able to deal with batteries anywhere near that large, then I’d imagine most of them would choose twenty times the battery life/ range over being able to charge fast enough overload a wall outlet/ small power plant.