That's a cute idea, but building accurate enough requirements to complete the task is actually part of the core problem. This team bypassed that bottleneck by i

That's a cute idea, but building accurate enough requirements to complete the task is actually part of the core problem. This team bypassed that bottleneck by ignoring requirements, re-building the application(s) 1:1, and then using testing to prove that they reproduced the same result(s) for the same input(s). In order to set up the competition you're suggestion the department would need to have documentation which they lack, which also happens to be the whole crux of the issue.