It's ok for most people but some just have more devices and want to switch them from time to time. Performing factory reset means compiling apps to aot, retransferring all apps the need to reconfigure all apps (Wear Mini Launcher, anyone?).
There used to be an app BeeLink but it stopped working and was removed.
There's actually way faster way how to set up connection with a new phone - in a minute. Just delete application data of "Google Play Services Wearable" app and reboot. All the 3rd party apps with their configurations, all watch faces with configurations, Google Fit data, and basically everything else will be kept.
Step by step
- Wear is connected with phone A so turn off Bluetooth on this phone.
- Execute following command (with Wear connected and ADB enabled - doesn't require root) or run attached app (root on watch required).
adb shell "pm clear com.google.android.gms && reboot"
- Power on Bluetooth on phone B.
- Depending whatever devices were paired previously, confirm pairing code or initiate new pairing using following command (thanks @matejdro) or also use the wear app for that
adb shell "am start -a android.bluetooth.adapter.action.REQUEST_DISCOVERABLE"
- Finish setup, let it work for some time and restart both phone B and your watch to properly apply all changes. Done.