Maybe you can have both a Li Ion and one of these, and you only sue the LiIon after the graphene one is depleted. That way, you can recharge quickly to a fraction of total power, and optionally wait longer for a full charge.
Maybe but both are going to take up space and the video isn't really clear on how much space the super-capacitor is going to need so you'll probably end up with the same problem of not having the same long life as just having the single slower charging Li Ion battery.