Same experience: 6S started shutting down at about 20% after less than a year. I recall searching for this problem and finding that Apple acknowledged that "it's a bug" and that they were working on a fix. The fix came out, but they didn't explain in what way: since then I have an underperforming 6S (50% of average geekbench score) and nobody told me why untill now. Totally agree with your guess of the reason: it was cheaper to do that in software than to replace a lot of batteries, also avoiding the PR nightmare.