Although I would agree that it is worth holding off on free sparring for white belts: I'll often stick with specific sparring when I teach (e.g., start in guard, person on the bottom tries to sweep or submit, person on top tries to pass. If either achieves their goal, restart in guard).
That's also what they did (presumably still do?) at RGA HQ . When I was there, lessons were split between beginner and advanced. In the beginner class, you only did specific sparring. Free sparring came in during the higher level classes.
That's exactly what we do at the Labs too. It works brilliantly and everybody learns
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