I think that we've just launched an app that is pretty much similar to what you described. It calls WorkoutNe and it is 1:1 live workouts with random partners from all over the world.
We have combined social facilitation and Japanese Kaizen practice to create an environment with the easiest threshold to enter regular physical activity on the market. Commitment to a real partner motivates you to come to training, and a simple exercise makes the process easy and joyful, so that you want to continue and gradually increase the physical activity.
Here you can read more:
Hope to see you on workouts! ;)