Apple Fitness+ Works on iPhone and iPad Without an Apple Watch
Apple designed the new Fitness+ service to work with a paired Apple Watch as the Apple Watch is meant to allow you to track your metrics while you follow along on a workout, but as it turns out, an Apple Watch isn't strictly necessary to use the Fitness+ app on an iPhone or iPad.
When starting a Fitness+ workout on iPhone or iPad when you're not wearing an Apple Watch, the app asks if you want to begin a workout without the watch. You can do the entire workout sans watch, but of course no metrics show up on the iPhone or iPad's display.
This is not, however, possible on Apple TV. When using Fitness+ with the Apple TV, Apple requires a synced and connected Apple Watch. Attempting to do a workout on Apple TV without the watch will only let you preview a workout, rather than begin one.
It's not clear why Apple is allowing workouts to be done on an iPhone or iPad without an Apple Watch while that same functionality does not work with the Apple TV, but the service was meant for an Apple Watch and isn't ideal for non-Apple Watch owners.