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OP,
I've read this whole thread, twice in fact, and the only thing I've come away with is that you very likely have some mistaken notion regarding how most portable electronic devices work and are designed... Honestly, reading both your posts I'm still unsure what you're really trying to ascertain.
A battery only device typically uses only replaceable one time use or rechargeable batteries, and may or may not have a charging circuit. If so, the charging circuit may not provide enough current to run the device without leaching power from the batteries as well. Less likely in modern designs, but possible.
Most modern devices with rechargeable batteries have AC(you'd say mains) or DC adaptors supplying sufficient current to run the device as well as charge the batteries -though it is far from unheard of that operating the device while charging leads to slower charging of the batteries... You may notice that some manufacturers will offer a lower current adaptor or power supply with a laptop that isn't capable of powering the device and charging quickey, or at all, but also offer a higher current or wattage unit capable of higher performance. Sometimes, it is felt that the lesser adaptor is preferred for portability as they are usually physically smaller and that having enough current to power the device for operation is more than sufficient.
It really comes down to how much current can be supplied to the device via the adaptor and how much current the device requires to operate. The surplus is available for charging, though may not be fully utilized as batteries can only be charged at certain rates based on their design and construction or overheating and rupture or explosion might occur due to gas overpressure or the like.
Personally, I tend to prefer adaptors sized to be able to power a device as needed while being able to charge the batteries at a reasonable rate. However, it is fair to note that everyone's idea of reasonable varies somewhat based on usage patterns, cost, and trying to pack and transport adaptors and other possibly needed peripherals, etc.
I'm a big fan of the current trend towards "nearly universal" acceptance of 5Vdc micro-USB adaptors for cell phones, tablets, and similar devices. I wish notebooks and laptops would join the movement, but laptop batteries tend to be of such high wattage that it would take quite a while to charge them even with a 5Vdc @ 2A charger. That's only a maximum of 10 watts per hour... My old Lenovo X200 laptop/tablet has a battery rated 14.8Vdc@5.2A that's nearly 80Watts! Assuming lossless conversion (80 to 95% is far more realistic) it'd take 8 full hours just to charge the battery with the laptop powered off.(more like 10 hours, or more, with typical losses.)
The other downside for designers and engineers is that higher currents require larger conductors, wider, heavier traces on pc boards, etc., so it seems somewhat unlikely that higher current, lower voltage batteries will become popular soon for higher wattage requirements. It's a shame though, as being able to use the same adaptor for everything would be pretty convenient and very handy in a pinch. As it is, I shall continue to be pleased just to have that ability with my tablet, e-ink reader, and cell phone.
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