I actually encountered this with my 6+, which I eventually upgraded. It was quickly depleting the battery, but the tests showed it was fine. The tech urged me to upgrade to the latest iOS, which I was hesitant to do, since I'd heard doing so would slow my phone. I didn't want a slow phone with a battery that died quickly. He assured me that the slowness had been addressed. Wanting to fix my phone, I upgraded. [0]
Immediate slowness, to the point of being unusable, demonstrated to the in-store techs. Launching Twitter, for instance, would take minutes and crash half the time. I then found there was no supported method of reverting the upgrade, though one tech told me that if I browsed YouTube I could find a tutorial. I didn't want to DIY a downgrade and still have the short battery life, so I ended up selling my phone for a very low price and buying a new one. If I'd known replacing the battery would have revived it, I'd have happily done that.