Underdiscussed point: one reason we want such high capacity power storage is that recharging takes hours. Society has internalized long charging times as normal. Would we fuss quite so much about run time if a recharge took seconds instead? (Am thinking cell phones/tablets here, not the dangerously high power issues of recharging a car in one minute flat.)
You can already buy flashlights with supercapacitors that have low run times but recharge in seconds, and there is a bus in China that recharges its supercapacitors at every stop. In addition they last for many times more discharge cycles.
For many applications, we can get the equivalent of fast recharging by swapping batteries. Yet, we still want long battery life because swapping is inconvenient.
Fast recharge is also inconvenient. Just as you must have a set of batteries to swap, you must have the means and opportunity to fast recharge. Note that a fast recharger is probably at least as big as a set of batteries. And, I can swap batteries in places where I can't plug in the recharger.
Yes, fast recharge is less inconvenient than slow recharge.
Quick thought experiment: right now, you can go out and buy a portable charger with a battery inside. For $40 or so, you can get one roughly the size of carrying a second smartphone with 5000mAh, which is several full charges for your average smartphone. You can throw it in a purse or spare pocket and have it when you need a charge and you're not near another power source.
It's not fiddly like opening the case of a phone and swapping out the battery, but the big problem with this is having to leave it hooked up while it charges if you're still using your phone. With fast recharge, this would go away. Hook it up for a minute, charge the phone up, unhook it, put it away. Easy peasy.
For me, at least, this would be a huge win. YMMV
Edited to add: with fast recharging, you could also recharge the portable charger itself if you ever come in contact with an outlet. So let's say you have two really long flights with a short layover. Find an outlet for a minute on the layover, recharge the charger, and you now have your charger ready to go for the next flight. Win.
I don't think swapping batteries is a good analog for fast recharge. For one, the cost of a kilowatt hour in AA batteries well exceeds $100, even buying in 20-count lots. From the wall, it costs less than a dollar. Swapping batteries is also significantly more effort than plugging in a microUSB or whatever.
Still way to cumbersome. I would love to be able to get a quick fix but I won't trade any battery life for it.
If I'm ever around to recharge quickly I can just as well let it sit there for a while, at least the vast majority of times. Please note how convenient it is to charge from a USB-port, a micro usb cable is all that is needed to be able to charge pretty much anywhere (and they are cheap enough leave one at home/work/laptop/pocket. With a fast charger I'd have to bring it along and plug it in everywhere - not worth it. And I most definitely would like at least the same poor battery life that we have today, otherwise you wouldn't be able to last a day without a charge and that it just unacceptable regardless of how easy or fast it is to recharge.
It sure won't be a microUSB port. To charge a middle-of-the-road 2500mAh capacity battery in, say, 10 seconds, you must flow something like 70A @ 5V, and that's ignoring the fact that capacitor charge curves are of the exponential decay variety (i.e. drastically higher initial power draw).
(A real-world application would probably kick up the voltage and lower the current, but USB is always 5V)