I actually started to hit this problem on my iPhone 5S. Not the slow down but the original issue that caused Apple to slow down phones. Old batteries that were really degraded would cause the phones to just die and shut off when the CPU had a spike in usage. I'm sure thats not great for the file system when that keeps happening. However it must be noted that it only started to occur after the phone was 5 years old and the battery had dropped to about 50% of its original design capacity. In fact this was one the reasons I eventually upgraded the phone...that plus I got a new job so it was time to finally upgrade the iPhone 5S to something better (a 1st gen iPhone SE ha ha). I could have just replaced the battery and continued using the 5S for another 1-2 years (as it had 1-2 more years of software updates from what I recall).