At the end of the day if the phone draws more power than the power source provides, you're limited to bursts of activity until the capacitor is depleted and then the phone is dead while the capacitor recharges. 0.2W is barely enough to power an idling phone, let alone charge an extra capacitor.
Today we juggle with ~15+Wh batteries (the "capacitor") and 30+W fast chargers (the "power source") and still need better.
It doesn't need to replace conventional charging. But a phone that gained charge when unused might still be useful - being able to make a call later might be better than never.
It would be great if used as an "emergency power source". I see this equivalent to the satellite SOS systems - not useful for daily use but essential in emergencies. You know you can get brief emergency function every x hours.
But for the question asked higher in the thread, it would never be comparable to a "real" battery. This would be a very special purpose battery.
Today we juggle with ~15+Wh batteries (the "capacitor") and 30+W fast chargers (the "power source") and still need better.