Here's a summary of the issues surrounding older iPhones and performance degradation with older batteries.
1. A small number of iPhones (6 and 6s, but 7 as well) had issues with sudden shutdowns.
2. The cause of these shutdowns was that under high CPU loads, older batteries were unable to deliver enough power and the phone would shut off.
3. Apple's solution to this was to throttle the CPU when phone with affected batteries were subjected to high power demands.
4. Then with the upgrade to iOS11, my belief is that more phones were affected because the baseline power usage of iOS11 was higher, so the number of phones affected by the throttling grew. (I never had a random shutdown on iOS10 and I don't believe I was ever throttled).
5. All of the above was never disclosed by Apple, other than vague explanations under the "What's New" tab of the iOS updates.
6. Some clever folks figured out that their phones were slowing down as the battery percentage (note this does not mean the battery capacity) ran down. With the power of social media, these clever guys figured out what Apple was doing.
7. These same clever folks figured out that when they put in a new battery, that could consistently deliver the high power needed under peak loads, the phones would not be throttled.
The fallout of this was that the narrative was that Apple was decpetively crippling otherwise good phones in order to drive people to upgrade. I think many people remembered back to the upgrade that killed iPhone4 and essentially bricked them.
So Apple response was to reduce the price of battery replacements from $80 to $30 for one year (plus a few months).
Note - iPhone batteries have always been replaceable, it's just not an easy process.
Note 2 - iOS11 will throttle if the phone experiences a sudden shutdown, but now you will be able to go into the settings to turn off the throttling, but you're risking further sudden shutdowns.