The problem is twofold: Firstly to compete with Lithium based powertanks, these things would need at least 2000mAh or so at 5V.
This would need an immense capacity which is not yet available in a form factor that would be usable as portable power tank.
Therefore the dubious project claims they'd use graphene supercapacitors which however are not commercially available yet.
E.g. there are supercaps available with 350F and 2.7V, but this means a meager 945 As or 0.2625 Ah.
Secondly, the currents needed to charge it quickly would be very high. E.g. with a traditional 1C approach, a 2000mAh Lithium based battery would be charged with 2A.
So you'd need 1h to charge it. It's easy to see that to bring this down to e.g. 1 minute, you'd need 60 times the current. So 120A for a 1 minute charge and still 24A for
a 5 minute charge time. These are current which are not so easily handled by small pocket size devices, especially if also the supercap should fit in there.