Great insight! Unsurprisingly, you're not the first. To my knowledge though, this method doesn't have a standard name and isn't prevalent. Predictions about others might give more information, but are still manipulable and hard to interpret when comparing respondents to each other. Did this person say lots of others cheat because they cheat or because they are bad with probabilities?

Alternatively, if you have a question with a single underlying answer, predictions about opinions are potentially useful for filtering out bias. This is the idea behind Prelec's Bayesian truth serum. Respondents maximize their payments from the system by being honest, and the group with the highest average scores tends be correct.