Because the capacity was diminished…. New batteries didn’t have this issues since they were… well new…and had the capacity.
In a fully charged battery you could run demanding stuff, it’s only when the charge depleted that it became an issue, which is it couldn’t acces the capacity for the extra voltage anymore.
Without capacity, you can’t provide the high current… they’re literally related and go hand in hand………
Again, you’re literally explaining more or less the same thing, in a far less technical way… so sure to a laymen you’re “correct”, but that’s where it ends.