You would have no idea cause Apple would just slow down your device instead.
I'm a developer. I write benchmark timing code to test my apps. I can figure out very accurately if a CPU was slower than before. My apps would run slower (lower frame rate, etc.) if the CPU was being throttled. They aren't.
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I have never heard of a device randomly shutting down because its battery was aged
Well I have, and have seen multiple old MacBooks, Windows laptops, Android and Palm devices that suddenly shutdown before the battery gauge goes below 5%.