Would 'charges in seconds, last for days' really be useful? Assuming #days = #seconds and 'lasts' = 'continuously delivers power', such a battery would require 86,400 times as much charging power as it delivers.
=> A 10Wh battery in a tablet that gets charged in a second would require over 30kW of power during that second.
The issue is there are so many of these "proof of concepts" that cannot be scaled for one reason or another. I'm vary wary of stories like this because they happen so frequently and often fizzle.
I agree, I just try to remain hopelessly optimistic. :)