The idea was to use a 5V solar panel like this
to charge a Li-Ion power bank which could then charge AA batteries or other devices that connect to USB to charge.
Well, I don't really need an analyzing charger per say. I want to see roughly how much energy is going into the batteries. I do like to fully discharge and recharge my Eneloops with the BC-700 though. I'm not sure of the current draw from 12V with 4 batteries charging at 700mA though. If the charger was reasonably efficient it could easily charge 4AA batteries at 700mA with like 6W of power. I guess I will measure the current draw of my BC-700 and see how much current it when charging.
I've got a 12vdc 60w (2x30w Monos) solar panel system feeding a Morningstar SS-10-L PWM digital controller and a couple of 22Ah/12Ah SLA/AGM mother batteries, so that's the way I roll in that system. My chargers are/were 12vdc, so I'm good there.
Then last year, after the 5v USB folding solar panels started flooding the market, I got a 14w jobbie, some Xtar USB chargers and some inexpensive power banks, to compliment the heavier system and cover some more bases.
The Anker Power Port 21w folder will be the next one I buy, unless something better comes out. Like 18650 cells, the manufacturers fudge the numbers a bit and if you get half the claimed output, you're lucky. So that 21w might actually be 10w-12w, which isn't a lot when charging up 4xAAs.
This being said, 12vdc rollable/foldable panels are substantially more money, although they might be the way to go for quicker charging.
There are always inefficiencies and people thinking that they're going to charge up 4 Eneloop batteries that are at 20% SOC, in a couple/few solar hours using some 10w solar jobbie are probably smoking some good stuff.
With solar, much like with fish tanks, buy the biggest panel that you can afford.
Using a 12vdc solar panel(s,) a digital controller (20w plus,) a mother battery and 12 volts can work fine, if not a bit on the bulkier/heavier side than a USB system.
Add to all of this, the fact that the BC-700 type chargers tend to trip their temperature safeties and I wouldn't rely on the BC-700 charger to charge up quickly in a SHTF event.
The VC4, your Anker PP 21w and some power banks that you can self replace the cells in and you're set for most small scale scenarios, IMO.