Synthetic data works better for robots since you can generate endless scenarios based on real physical laws.
When we (ZenRobotics) tried this 15 years ago a big problem was the creation of sufficiently high-fidelity simulated worlds. Gathering statistics and modelling the geometry, brittleness, flexibility, surface texture, friction, variable density etc of a sufficiently large variety of objects was harder than gathering data from the real world.
Example of modern physics simulation: https://www.youtube.com/watch?v=7NF3CdXkm68
I believe this is the most popular tool now: https://github.com/google-deepmind/mujoco
AFAICT these have not resulted in any shipping products.