For extremely short duration peaks up to a few microseconds capacitors are a great workaround. They are necessary for pretty much every digital integrated circuit. A billion transistors all switching at the same time on the rising edge of a clock cycle has a massive instantaneous current draw.
Yes. And it does look like a case of undersized batteries. If I had to guess, I'd say it was because of too strict product design specifications meeting a lower than expected quality in manufacturing.
CPU power peaks usually last for a (large) fraction of a millisecond or more, because that's how the OS scheduler works. Added to that, peaks may not happen for entire minutes or hours. Both of those work against the usefulness of large capacitor banks.
If they are related (and perhaps they are, I wasn't thinking about the recall when I wrote my comment), do you think it's unreasonable for engineers at Apple to try to prevent unexpected shutdowns? I would think it would be unreasonable not to, once they saw the impact it was having on user experience. And that's besides improving the battery. The amount of engineering that goes on with respect to power and performance management is incredible, and attacking these types of problems from multiple angles is expected, particularly when you're looking to eek out even more performance in something that's already been through years of optimization iterations.
Apple knew the peak draw of their SoC (they designed it). And they knew the capabilities of the battery. Under sizing the battery is exactly what I would call a design flaw.