I sometimes use my phone for running or walking with the watch connected for HR tracking. When I look at the workout details after I'm done, I don't see the VO2 max or running metrics although the watch is connected. I suggest that you add an option or even by default use the watch for these metrics when connected to the phone for a workout. That way we can use the most out of the watch.
Please notice that sometimes it's better to use the phone for a workout especially when I'm trying to follow a running plan.
