One theory for why your iPhone 6s Plus is stuck on a black screen after updating to iOS 10 is that something in the phone's present system setup is incompatible with the new platform, resulting in the device's strange state.
Insufficient memory or the remaining accessible storage space on your iPhone is not enough to allocate the actual file size of the update is another possible explanation why your iPhone is stuck on a black screen with a spinning circle. As a consequence, performance issues such as an iPhone that is sluggish, unresponsive, frozen, won't turn on, or powers on but can't get beyond the start-up process may arise.