Apple's choice was not between slowdowns and random shutdowns, but between informing users or keeping them unaware that a battery swap could keep the phone fast

Apple's choice was not between slowdowns and random shutdowns, but between informing users or keeping them unaware that a battery swap could keep the phone fast. Also the slowdowns weren't "less noticeable" in some cases, I've seen iPhones that reached a point where processing a single touch input could take up to 5 seconds. Customers were generally not aware what the fix for the slowdown was. No non-technical person would ever think of swapping the battery because of slower performance, in my experience most people assume that the storage is full or the system is bloated. For a random user the only known guaranteed fix is buying a new phone. So Apple had an incentive to not inform users because of that and they clearly didn't mind.