I heard the old batteries, when giving high current would depress voltage long enought to trigger the shutdown, plausibly long enough to mess up the processor if it didn't shut down, but could genuinely give a lower current for a long time, such that rounding the charge down to zero would be harmful. It's easy to argue it's better to keep the phone slower then just shut it down when it can't reliably go fast.

But it’s not a matter of total charge, but output, hence it shutting down even though there’s plenty of stored energy in the battery.